0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.32 % Computer : n028.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % DateTime : Thu Jul 2 09:16:07 EDT 2020 0.11/0.32 % CPUTime : 19.62/19.81 ============================== Prover9 =============================== 19.62/19.81 Prover9 (32) version 2009-11A, November 2009. 19.62/19.81 Process 7769 was started by sandbox2 on n028.cluster.edu, 19.62/19.81 Thu Jul 2 09:16:22 2020 19.62/19.81 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_7576_n028.cluster.edu". 19.62/19.81 ============================== end of head =========================== 19.62/19.81 19.62/19.81 ============================== INPUT ================================= 19.62/19.81 19.62/19.81 % Reading from file /tmp/Prover9_7576_n028.cluster.edu 19.62/19.81 19.62/19.81 set(prolog_style_variables). 19.62/19.81 set(auto2). 19.62/19.81 % set(auto2) -> set(auto). 19.62/19.81 % set(auto) -> set(auto_inference). 19.62/19.81 % set(auto) -> set(auto_setup). 19.62/19.81 % set(auto_setup) -> set(predicate_elim). 19.62/19.81 % set(auto_setup) -> assign(eq_defs, unfold). 19.62/19.81 % set(auto) -> set(auto_limits). 19.62/19.81 % set(auto_limits) -> assign(max_weight, "100.000"). 19.62/19.81 % set(auto_limits) -> assign(sos_limit, 20000). 19.62/19.81 % set(auto) -> set(auto_denials). 19.62/19.81 % set(auto) -> set(auto_process). 19.62/19.81 % set(auto2) -> assign(new_constants, 1). 19.62/19.81 % set(auto2) -> assign(fold_denial_max, 3). 19.62/19.81 % set(auto2) -> assign(max_weight, "200.000"). 19.62/19.81 % set(auto2) -> assign(max_hours, 1). 19.62/19.81 % assign(max_hours, 1) -> assign(max_seconds, 3600). 19.62/19.81 % set(auto2) -> assign(max_seconds, 0). 19.62/19.81 % set(auto2) -> assign(max_minutes, 5). 19.62/19.81 % assign(max_minutes, 5) -> assign(max_seconds, 300). 19.62/19.81 % set(auto2) -> set(sort_initial_sos). 19.62/19.81 % set(auto2) -> assign(sos_limit, -1). 19.62/19.81 % set(auto2) -> assign(lrs_ticks, 3000). 19.62/19.81 % set(auto2) -> assign(max_megs, 400). 19.62/19.81 % set(auto2) -> assign(stats, some). 19.62/19.81 % set(auto2) -> clear(echo_input). 19.62/19.81 % set(auto2) -> set(quiet). 19.62/19.81 % set(auto2) -> clear(print_initial_clauses). 19.62/19.81 % set(auto2) -> clear(print_given). 19.62/19.81 assign(lrs_ticks,-1). 19.62/19.81 assign(sos_limit,10000). 19.62/19.81 assign(order,kbo). 19.62/19.81 set(lex_order_vars). 19.62/19.81 clear(print_given). 19.62/19.81 19.62/19.81 % formulas(sos). % not echoed (7934 formulas) 19.62/19.81 19.62/19.81 ============================== end of input ========================== 19.62/19.81 19.62/19.81 % From the command line: assign(max_seconds, 960). 19.62/19.81 19.62/19.81 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 19.62/19.81 19.62/19.81 % Formulas that are not ordinary clauses: 19.62/19.81 1 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 2 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 3 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 4 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 5 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 6 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 7 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 8 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 9 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 10 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 11 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 12 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 13 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 14 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 15 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 16 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 17 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 18 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 19 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 20 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 21 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__ABSTRACT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 22 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f160_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 23 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),f165_1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f165_1_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef165_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 24 (all V0y_2E0 all V1x_2E0 ((p(s(tyop_2Emin_2Ebool,V0y_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))) -> (-p(s(tyop_2Emin_2Ebool,V1x_2E0)) -> -p(s(tyop_2Emin_2Ebool,V0y_2E0))))) # label(thm_2Ebool_2EMONO__NOT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 25 (all A_27a all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f144_0_2E1(s(A_27a,V0a_2E0))))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 26 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 27 (all A_27a all V0P_2E0 all V1Q_2E0 (((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) <-> (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) & ((all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))) & ((all V7x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V7x_2E0)))))) <-> (all V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V6x_2E0))))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0))))) # label(thm_2Ebool_2EPULL__FORALL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 28 (all A_27a all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))))) # label(thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 29 (all A_27a all V0x_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f71_0_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 30 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 31 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f154_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 32 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 33 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 ((p(s(tyop_2Emin_2Ebool,V2Q_2E0)) -> s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1P_27_2E0)) & (p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V3Q_27_2E0) = s(tyop_2Emin_2Ebool,V2Q_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,V2Q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) & p(s(tyop_2Emin_2Ebool,V3Q_27_2E0))))) # label(thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 34 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2Eliteral__case__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 35 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f29_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef29_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 36 (all A_27a all A_27b all A_27c all V0b_2E0 all V1N_2E0 all V2M_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),f122_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0))),s(A_27a,V2M_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f122_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0))),s(A_27a,V2M_2E0))),s(A_27b,V0b_2E0)))) # label(thm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 37 (all A_27a all V0P_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,f158_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0)))))) # label(def1_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 38 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebool_2Eitself_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 39 (all A_27a all V0x_2E0 ((all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 40 (all A_27a all V0t_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,f155_0_2E2(s(tyop_2Emin_2Ebool,V0t_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 41 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V2C_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) & p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2ERIGHT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 42 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,f168_0_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))),f168_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef168_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 43 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 44 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f154_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f154_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef154_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 45 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 46 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))) <-> (-p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t2_2E0))) & (p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t1_2E0))))) # label(thm_2Ebool_2ECOND__EXPAND__IMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 47 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 all V3x_27_2E0 all V4y_2E0 all V5y_27_2E0 (s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1Q_2E0) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0)) & (-p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V5y_27_2E0) = s(A_27a,V4y_2E0)) -> s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1Q_2E0),s(A_27a,V3x_27_2E0),s(A_27a,V5y_27_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(A_27a,V2x_2E0),s(A_27a,V4y_2E0))))) # label(thm_2Ebool_2Ebool__case__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 48 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 49 (all A_27a all V0x_2E0 all V1x_27_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))) # label(thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 50 (all V0t_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 51 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f121_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),f121_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ef121_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 52 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 53 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 54 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Ebool_2EIMP__F__EQ__F) # label(axiom) # label(non_clause). [assumption]. 19.62/19.81 55 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> ((all V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) -> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2EBOTH__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 56 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f71_0_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0)))) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(def0_2Ethm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 57 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) | p(s(tyop_2Emin_2Ebool,V1Q_2E0)) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) | p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2ELEFT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 58 (all A_27a all V0P_2E0 all V1Q_2E0 (((exists V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))) & ((exists V7x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V7x_2E0)))))) <-> (exists V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V6x_2E0))))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0))) & (((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))))))) # label(thm_2Ebool_2EPULL__EXISTS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 59 (all A_27a all A_27b all V0b_2E0 all V1f_2E0 all V2g_2E0 all V3x_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0),s(A_27a,V3x_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0))),s(A_27a,V3x_2E0)))) # label(thm_2Ebool_2ECOND__ABS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 60 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 ((all V2x_27_2E0 all V3x_27_27_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V2x_27_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V3x_27_27_2E0))) -> s(A_27b,V2x_27_2E0) = s(A_27b,V3x_27_27_2E0))) & (all V4x_2E0 ((exists V5x_27_2E0 s(A_27a,V4x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V5x_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V4x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0)))))) # label(thm_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 61 (all A_27a all V0P_2E0 all V1f_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ebool_2ERES__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 62 (all V0t_2E0 (((p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) & ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 63 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2M_2E0 all V3N_2E0 ((all V4x_2E0 (s(A_27a,V4x_2E0) = s(A_27a,V3N_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V4x_2E0))))) & s(A_27a,V3N_2E0) = s(A_27a,V2M_2E0) -> s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2M_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V3N_2E0))))) # label(thm_2Ebool_2ELET__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 64 (all A_27a all A_27b all V1N_2E0 all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0))) = s(A_27b,f121_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 65 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0))))) & (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Ebool_2EFORALL__AND__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 66 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f70_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f70_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef70_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 67 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V1B_2E0)) & p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) & (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V2C_2E0))))) # label(thm_2Ebool_2ELEFT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 68 (all A_27a all V0Q_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,V0Q_2E0)) | (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,V0Q_2E0)))))) # label(thm_2Ebool_2ELEFT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 69 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 70 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f71_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f71_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef71_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 71 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f161_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 72 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 (s(A_27a,V2z_2E0) = s(A_27a,V1y_2E0) & s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) -> s(A_27a,V0x_2E0) = s(A_27a,V2z_2E0))) # label(thm_2Ebool_2EEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 73 (all A_27a all V0g_2E0 all V1f_2E0 all V2Q_2E0 all V3P_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0) -> ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0)))))) # label(thm_2Ebool_2ERES__EXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 74 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2Eitself__case_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))),s(A_27b,X1_2E0))) = s(A_27b,c_2Ebool_2Eitself__case_2E2(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eitself__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 75 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V2C_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0))) & (p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0))))) # label(thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 76 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f121_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,f121_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef121_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 77 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) | p(s(tyop_2Emin_2Ebool,V0P_2E0)))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) | p(s(tyop_2Emin_2Ebool,V0P_2E0)))) # label(thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 78 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef154_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 79 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 80 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0)) # label(thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 81 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 82 (all X0_2E0 s(tyop_2Emin_2Ebool,f163_3_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_3_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_3_2E1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 83 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 84 (all A_27a all A_27b all V0P_2E0 all V1rep_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) <-> (exists V5x_27_2E0 s(A_27a,V4x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0),s(A_27b,V5x_27_2E0)))))) & (all V2x_27_2E0 all V3x_27_27_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0),s(A_27b,V2x_27_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0),s(A_27b,V3x_27_27_2E0))) -> s(A_27b,V2x_27_2E0) = s(A_27b,V3x_27_27_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0)))))) # label(thm_2Ebool_2ETYPE__DEFINITION__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 85 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2x_2E0)))))) -> ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) -> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Ebool_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 86 (all A_27a all V0x_2E0 all V1x_27_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) # label(thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 87 (all A_27a all V0P_2E0 (-(all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) <-> (exists V2x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 88 (all A_27a all A_27b all A_27c all V0P_2E0 all V1N_2E0 all V2M_2E0 s(A_27c,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),f165_1_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f165_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0)))))) # label(thm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 89 (all V1b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f163_0_2E1(s(tyop_2Emin_2Ebool,V1b_2E0)))) # label(def1_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 90 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f121_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f121_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef121_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 91 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(thm_2Ebool_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 92 (all A_27a all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 all V3x_2E0 ((s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) -> s(A_27a,V3x_2E0) = s(A_27a,V1x_27_2E0)) & (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) -> s(A_27a,V2x_27_27_2E0) = s(A_27a,V3x_2E0)) <-> p(s(tyop_2Emin_2Ebool,f21_0_2E4(s(tyop_2Emin_2Ebool,V0x_2E0),s(A_27a,V1x_27_2E0),s(A_27a,V2x_27_27_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 93 (all A_27a all V0g_2E0 all V1f_2E0 all V2Q_2E0 all V3P_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0) -> ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ebool_2ERES__FORALL__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 94 (all A_27a all A_27b all V0t_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2EETA__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 95 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2ERES__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 96 (all A_27a all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f160_0_2E0)))) # label(thm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 97 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 ((p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) & (p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0))) -> (p(s(tyop_2Emin_2Ebool,V2x_2E0)) & p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0)) & p(s(tyop_2Emin_2Ebool,V3w_2E0))))) # label(thm_2Ebool_2EMONO__AND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 98 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2EDISJ__COMM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 99 (all A_27a all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f161_0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 100 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) <-> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 101 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) | (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 102 (all A_27a all V0i_2E0 s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0) = s(tyop_2Ebool_2Eitself(A_27a),V0i_2E0)) # label(thm_2Ebool_2EITSELF__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 103 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0)))))) # label(thm_2Ebool_2ECOND__RAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 104 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 105 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ERES__ABSTRACT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 106 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 107 (all A_27a all V1Q_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,f154_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0)))) # label(def1_2Ethm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 108 (all A_27a all A_27b all V0u_2E0 all V1t_2E0 all V2a_2E0 s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f168_0_2E3(s(A_27a,V2a_2E0),s(A_27b,V1t_2E0),s(A_27b,V0u_2E0))),s(A_27a,V2a_2E0))) = s(A_27b,V1t_2E0)) # label(thm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 109 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f121_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f121_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef121_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 110 (all A_27a all V0t1_2E0 all V1t2_2E0 exists V2fn_2E0 (s(A_27a,V1t2_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V2fn_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V2fn_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(A_27a,V0t1_2E0))) # label(thm_2Ebool_2EboolAxiom) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 111 (all A_27a all V0a_2E0 exists V1x_2E0 s(A_27a,V0a_2E0) = s(A_27a,V1x_2E0)) # label(thm_2Ebool_2EEXISTS__REFL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 112 (all A_27a all A_27b all V0f_2E0 ((all V1x1_2E0 all V2x2_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x1_2E0))) -> s(A_27a,V1x1_2E0) = s(A_27a,V2x2_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))) # label(thm_2Ebool_2EONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 113 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f166_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f166_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ef166_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 114 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f21_0_2E4(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f21_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef21_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 115 (all A_27a all A_27b all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) <-> (all V1y_2E0 exists V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,V1y_2E0)))) # label(thm_2Ebool_2EONTO__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 116 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f160_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,f160_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef160_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 117 (all A_27a all V0x_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 118 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Ebool_2ELEFT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 119 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f122_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27c,f122_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef122_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 120 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 121 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2EAND2__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 122 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 123 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 124 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 125 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 126 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 127 (all V0bool_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0bool_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(thm_2Ebool_2EDATATYPE__BOOL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 128 (all A_27a all V0x_2E0 all V1x_27_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f30_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))))) = s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) # label(thm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 129 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f155_0_2E1(s(tyop_2Emin_2Ebool,V0t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & (all V2x_2E0 all V3y_2E0 s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0)))) # label(thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 130 (all V3b_2E0 s(tyop_2Emin_2Ebool,f163_2_2E1(s(tyop_2Emin_2Ebool,V3b_2E0))) = s(tyop_2Emin_2Ebool,V3b_2E0)) # label(def3_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.82 131 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 132 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 133 (all V0A_2E0 all V1B_2E0 (-p(s(tyop_2Emin_2Ebool,V1B_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> -(p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,V1B_2E0))))) # label(thm_2Ebool_2ENOT__IMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 134 (all A_27a all V0P_2E0 all V1a_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & s(A_27a,V2x_2E0) = s(A_27a,V1a_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))))) # label(thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 135 (all V2b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f163_1_2E1(s(tyop_2Emin_2Ebool,V2b_2E0)))) # label(def2_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 136 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f158_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f158_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef158_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 137 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef154_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 138 (all A_27a all A_27b all V0b_2E0 s(A_27b,c_2Ebool_2Eitself__case_2E2(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0),s(A_27b,V0b_2E0))) = s(A_27b,V0b_2E0)) # label(thm_2Ebool_2Eitself__case__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 139 (all A_27a all A_27b all A_27c all V1N_2E0 all V0b_2E0 all V4x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V4x_2E0))),s(A_27b,V0b_2E0))) = s(A_27c,f122_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 140 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f161_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f161_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef161_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 141 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EBOUNDED_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EBOUNDED_2E1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 142 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) | -p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & -p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> s(tyop_2Emin_2Ebool,V1t2_2E0) = s(tyop_2Emin_2Ebool,V0t1_2E0))) # label(thm_2Ebool_2EEQ__EXPAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 143 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebool_2EONTO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 144 (all A_27a all A_27b all V2a_2E0 all V1t_2E0 all V0u_2E0 all V3x_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f168_1_2E2(s(A_27a,V3x_2E0),s(A_27a,V2a_2E0))),s(A_27b,V1t_2E0),s(A_27b,V0u_2E0))) = s(A_27b,f168_0_2E4(s(A_27a,V2a_2E0),s(A_27b,V1t_2E0),s(A_27b,V0u_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 145 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EAND1__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 146 (all V0x_2E0 (-p(s(tyop_2Emin_2Ebool,V0x_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Ebool_2ENOT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 147 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 148 (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E1(s(tyop_2Emin_2Ebool,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2EBOUNDED__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 149 (all A_27a all V3x_2E0 all V2a_2E0 (s(A_27a,V3x_2E0) = s(A_27a,V2a_2E0) <-> p(s(tyop_2Emin_2Ebool,f168_1_2E2(s(A_27a,V3x_2E0),s(A_27a,V2a_2E0)))))) # label(def0_2Ethm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 150 (all A_27a all A_27b all A_27c all V1N_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),f122_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 151 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 ((p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0))) & (p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) -> (p(s(tyop_2Emin_2Ebool,V2x_2E0)) | p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0)) | p(s(tyop_2Emin_2Ebool,V1y_2E0))))) # label(thm_2Ebool_2EMONO__OR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 152 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f125_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0))) & (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 153 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t3_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t3_2E0)))))) # label(thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 154 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 all V3x_27_2E0 all V4y_2E0 all V5y_27_2E0 (s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1Q_2E0) & (-p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V5y_27_2E0) = s(A_27a,V4y_2E0)) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0)) -> s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1Q_2E0),s(A_27a,V3x_27_2E0),s(A_27a,V5y_27_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(A_27a,V2x_2E0),s(A_27a,V4y_2E0))))) # label(thm_2Ebool_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 155 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f29_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef29_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 156 (all V0P_2E0 ((all V1b_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))))) # label(thm_2Ebool_2EFORALL__BOOL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 157 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef29_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 158 (all A_27a all A_27b all A_27c all V0P_2E0 all V1N_2E0 all V4x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0))))) = s(A_27c,f165_1_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 159 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Ebool_2EDATATYPE__TAG__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 160 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f154_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef154_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 161 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,f163_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_0_2E1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 162 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef29_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 163 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f30_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f30_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef30_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 164 (all V0x_2E0 all V1x_27_2E0 ((all V2t_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t_2E0))) -> p(s(tyop_2Emin_2Ebool,V2t_2E0))))) <-> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) | p(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Ebool_2EOR__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 165 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 166 (all A_27a all V0b_2E0 all V1t_2E0 s(A_27a,V1t_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0)))) # label(thm_2Ebool_2ECOND__ID) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 167 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),f165_1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(A_27c,f165_1_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef165_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 168 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef158_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 169 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1t1_2E0)) & p(s(tyop_2Emin_2Ebool,V0b_2E0)) | -p(s(tyop_2Emin_2Ebool,V0b_2E0)) & p(s(tyop_2Emin_2Ebool,V2t2_2E0)))) # label(thm_2Ebool_2ECOND__EXPAND__OR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 170 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 171 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0))))) # label(thm_2Ebool_2EAND__INTRO__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 172 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0)) # label(thm_2Ebool_2EEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 173 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 174 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 175 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) | p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EOR__INTRO__THM1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 176 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) | (all V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Ebool_2EBOTH__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 177 (all A_27a all A_27b all V0t_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 178 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 179 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 180 (all A_27a all A_27b all A_27c all V1N_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),f166_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 181 (all A_27a all V0P_2E0 all V1f_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f159_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 182 (all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) & p(s(tyop_2Emin_2Ebool,V0x_2E0)) <-> (all V2t_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,V2t_2E0)))))) # label(thm_2Ebool_2EAND__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 183 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f154_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef154_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 184 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0)))) <-> (all V1y_2E0 exists V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V2x_2E0))) = s(A_27b,V1y_2E0)))) # label(thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 185 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f29_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f29_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef29_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 186 (all A_27a all A_27b all V0P_2E0 ((all V1x_2E0 all V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> (all V3y_2E0 all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V3y_2E0))))))) # label(thm_2Ebool_2ESWAP__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 187 (all V0A_2E0 all V1B_2E0 (-p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,V1B_2E0))))) # label(thm_2Ebool_2EIMP__DISJ__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 188 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 189 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f159_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f159_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef159_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 190 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 191 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) & (all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V2y_2E0)))) -> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 192 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) & (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ebool_2ESELECT__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 193 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ELEFT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 194 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(thm_2Ebool_2EFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 195 (all V0t1_2E0 all V1t2_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0))) -> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 196 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) -> (all V1b_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))))))) # label(thm_2Ebool_2Ebool__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 197 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f155_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f155_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef155_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 198 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f144_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f144_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef144_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 199 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f158_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef158_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 200 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f70_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 201 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f154_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef154_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 202 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 203 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),f168_0_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))),f168_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef168_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 204 (all A_27a all V0f_2E0 all V1v_2E0 ((all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1v_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1v_2E0)))))) # label(thm_2Ebool_2EUNWIND__FORALL__THM1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 205 (all A_27a all A_27b all V0f_2E0 all V1y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1y_2E0)))) # label(thm_2Ebool_2EBETA__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 206 (all V0A_2E0 all V1B_2E0 ((p(s(tyop_2Emin_2Ebool,V1B_2E0)) -> p(s(tyop_2Emin_2Ebool,V0A_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0))))) # label(thm_2Ebool_2EOR__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 207 (all A_27a all V0P_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,f154_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) # label(def2_2Ethm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 208 (all A_27a all V0P_2E0 all V1f_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f159_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 209 (all A_27a all V0P_2E0 all V1Q_2E0 (((all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2ELEFT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 210 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2ELET__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 211 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f122_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f122_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ef122_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 212 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f125_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f125_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef125_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 213 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 214 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 215 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 216 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2EBOTH__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.83 217 (all A_27a all V1f_2E0 all V3x_2E0 all V4y_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0)) <-> p(s(tyop_2Emin_2Ebool,f158_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))))) # label(def0_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 218 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 219 (all A_27a all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2ERES__FORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 220 (all A_27a all A_27b all V0P_2E0 ((exists V1x_2E0 exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> (exists V3y_2E0 exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V3y_2E0))))))) # label(thm_2Ebool_2ESWAP__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 221 (all A_27a all V0P_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) # label(thm_2Ebool_2EEXISTS__itself) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 222 (all A_27a all A_27b all V1N_2E0 all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0))) = s(A_27b,f165_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 223 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 224 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 225 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f71_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f71_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef71_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 226 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 227 (all V0f_2E0 ((all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V2x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) | (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V4x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V4x_2E0)))) | (all V3x_2E0 s(tyop_2Emin_2Ebool,V3x_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V3x_2E0)))) | (all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))))) # label(thm_2Ebool_2EBOOL__FUN__CASES__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 228 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 229 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 230 (all A_27a all V0P_2E0 all V1Q_2E0 (((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2ELEFT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 231 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) <-> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 232 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 233 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V3Q_27_2E0) = s(tyop_2Emin_2Ebool,V2Q_2E0)) & s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1P_27_2E0) -> (p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) | p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2ELEFT__OR__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 234 (all A_27a all A_27b all V0e_2E0 exists V1f_2E0 s(A_27b,V0e_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27b),V1f_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) # label(thm_2Ebool_2Eitself__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 235 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),f122_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f122_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef122_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 236 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),f166_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f166_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef166_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 237 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f144_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f144_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef144_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 238 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f155_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f155_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef155_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 239 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 240 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),f165_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f165_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ef165_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 241 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 242 (all A_27a all A_27b all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,V0t1_2E0)) # label(thm_2Ebool_2EABS__SIMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 243 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2M_2E0 all V3N_2E0 (s(A_27a,V3N_2E0) = s(A_27a,V2M_2E0) & (all V4x_2E0 (s(A_27a,V4x_2E0) = s(A_27a,V3N_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))) -> s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2M_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V3N_2E0))))) # label(thm_2Ebool_2Eliteral__case__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 244 (all A_27a all V0f_2E0 all V1v_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1v_2E0)))) <-> (all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1v_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2EUNWIND__FORALL__THM2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 245 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 246 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)) & (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 247 (all A_27a all X0_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 248 (all V0t1_2E0 all V1t2_2E0 ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0))) <-> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0))) # label(thm_2Ebool_2EEQ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 249 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2Ebool_2EEQ__EXT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 250 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f166_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f166_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef166_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 251 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,f70_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 252 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0)))) <-> (all V1x1_2E0 all V2x2_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V2x2_2E0))) -> s(A_27a,V2x2_2E0) = s(A_27a,V1x1_2E0))))) # label(thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 253 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 254 (all A_27a all A_27b all V0P_2E0 ((exists V1rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0))))) -> (exists V2rep_2E0 exists V3abs_2E0 ((all V5r_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5r_2E0)))) <-> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3abs_2E0),s(A_27a,V5r_2E0))))) = s(A_27a,V5r_2E0))) & (all V4a_2E0 s(A_27b,V4a_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3abs_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4a_2E0)))))))))) # label(thm_2Ebool_2EABS__REP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 255 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 256 (all A_27a all V1x_27_2E0 all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,f29_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V4y_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 257 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f21_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f21_0_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef21_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 258 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2x_2E0)))))) -> ((all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Ebool_2EMONO__ALL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 259 (all X0_2E0 s(tyop_2Emin_2Ebool,f163_2_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_2_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_2_2E1) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 260 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2ECONJ__SYM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 261 (all A_27a all V0t_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 262 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 263 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 264 (all A_27a all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0x_2E0),s(A_27a,V1x_27_2E0),s(A_27a,V2x_27_27_2E0))) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f21_0_2E3(s(tyop_2Emin_2Ebool,V0x_2E0),s(A_27a,V1x_27_2E0),s(A_27a,V2x_27_27_2E0)))))) # label(thm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 265 (all A_27a all V0P_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) # label(thm_2Ebool_2EFORALL__itself) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 266 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ERES__SELECT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__SELECT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 267 (all A_27a all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ebool_2ESELECT__AX) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 268 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,c_2Ebool_2EARB_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),V0rep_2E0))))) # label(thm_2Ebool_2Eitself__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 269 (all A_27a all V0x_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f72_0_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 270 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2Ebool_2ELET__DEF) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 271 (all V4b_2E0 (p(s(tyop_2Emin_2Ebool,f163_3_2E1(s(tyop_2Emin_2Ebool,V4b_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V4b_2E0)))) # label(def0_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 272 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f125_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f125_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef125_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 273 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 274 (all V0t_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,V2t2_2E0)) | p(s(tyop_2Emin_2Ebool,V1t1_2E0)) -> ((p(s(tyop_2Emin_2Ebool,V1t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V2t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))))) # label(thm_2Ebool_2EOR__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 275 (all A_27a all V0P_2E0 all V1t_2E0 ((all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1t_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Ebool_2EJRH__INDUCT__UTIL) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 276 (all A_27a all V0f_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0)))) -> ((all V4x_2E0 all V5y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> (all V6x_2E0 all V7y_2E0 all V8z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V7y_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V6x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_2E0))))))))) # label(thm_2Ebool_2ELCOMM__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 277 (all A_27a all V0P_2E0 (-(exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) <-> (all V2x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 278 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V2t3_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V2t3_2E0)))) # label(thm_2Ebool_2ECONJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 279 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 ((p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) & (p(s(tyop_2Emin_2Ebool,V1y_2E0)) -> p(s(tyop_2Emin_2Ebool,V2x_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V0z_2E0))) -> (p(s(tyop_2Emin_2Ebool,V1y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0)))))) # label(thm_2Ebool_2EMONO__IMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 280 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f158_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef158_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 281 (all V0P_2E0 all V1Q_2E0 all V2R_2E0 ((p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))))) # label(thm_2Ebool_2EDISJ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 282 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V1t1_2E0)) | -p(s(tyop_2Emin_2Ebool,V0b_2E0))) & (p(s(tyop_2Emin_2Ebool,V2t2_2E0)) | p(s(tyop_2Emin_2Ebool,V0b_2E0))))) # label(thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 283 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.62/19.84 284 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,f166_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f166_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef166_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 285 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 286 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f29_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef29_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 287 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,f72_0_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0)))))) # label(def0_2Ethm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 288 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f158_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef158_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 289 (all A_27a all V0t1_2E0 all V1t2_2E0 (s(A_27a,V1t2_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) & s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V0t1_2E0))) # label(thm_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 290 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef158_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 291 (all A_27a all A_27b all A_27c all V0b_2E0 all V1N_2E0 all V2M_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f166_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0))),s(A_27a,V2M_2E0))),s(A_27b,V0b_2E0))) = s(A_27c,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),f166_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0))),s(A_27a,V2M_2E0)))) # label(thm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 292 (all V0A_2E0 all V1B_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,V1B_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2EDISJ__EQ__IMP) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 293 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 294 (all A_27a all A_27b all V0P_2E0 all V1N_2E0 all V2M_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f121_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f121_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0)))))) # label(thm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 295 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 296 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f159_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f159_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef159_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 297 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0))) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2EBOTH__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 298 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 299 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 (s(tyop_2Emin_2Ebool,V1x_27_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) & (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> s(tyop_2Emin_2Ebool,V3y_27_2E0) = s(tyop_2Emin_2Ebool,V2y_2E0)) -> ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))))) # label(thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 300 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,f125_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 19.62/19.85 301 (all A_27a all V0x_2E0 all V1x_27_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f30_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(def0_2Ethm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 302 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 303 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) -> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 304 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 all V4b_2E0 ((p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V4b_2E0),s(tyop_2Emin_2Ebool,V2x_2E0),s(tyop_2Emin_2Ebool,V0z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V4b_2E0),s(tyop_2Emin_2Ebool,V1y_2E0),s(tyop_2Emin_2Ebool,V3w_2E0)))))))) # label(thm_2Ebool_2EMONO__COND) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 305 (all A_27a all V1f_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f158_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 306 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) & p(s(tyop_2Emin_2Ebool,V0P_2E0)) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 307 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V2Q_2E0) = s(tyop_2Emin_2Ebool,V3Q_27_2E0)) & (-p(s(tyop_2Emin_2Ebool,V2Q_2E0)) -> s(tyop_2Emin_2Ebool,V1P_27_2E0) = s(tyop_2Emin_2Ebool,V0P_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,V2Q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) | p(s(tyop_2Emin_2Ebool,V1P_27_2E0))))) # label(thm_2Ebool_2EOR__CONG) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 308 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2ECONJ__COMM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 309 (all A_27a all V0P_2E0 all V1x_2E0 ((all V2y_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2y_2E0)))))) -> s(A_27a,V1x_2E0) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) # label(thm_2Ebool_2ESELECT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 310 (all V0A_2E0 all V1B_2E0 all V2C_2E0 ((p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2C_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2ELEFT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 311 (all A_27a all A_27b ((all V0p_2E0 all V1m_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_2E0))))) & (all V3p_2E0 all V4m1_2E0 all V5m2_2E0 ((all V6x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4m1_2E0),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5m2_2E0),s(A_27a,V6x_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5m2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4m1_2E0))))))) # label(thm_2Ebool_2ERES__ABSTRACT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 312 (all A_27a all V0x_2E0 all V1x_27_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,f29_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0)))))) # label(def1_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 313 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 314 (all A_27a all A_27b all V0P_2E0 ((all V1x_2E0 exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> (exists V3f_2E0 all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Ebool_2ESKOLEM__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 315 (all V0y_2E0 all V1x_2E0 ((-p(s(tyop_2Emin_2Ebool,V1x_2E0)) -> -p(s(tyop_2Emin_2Ebool,V0y_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0y_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))))) # label(thm_2Ebool_2EMONO__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 316 (all V0v_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E1(s(tyop_2Emin_2Ebool,V0v_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 317 (all A_27a all A_27b all V0b_2E0 all V1f_2E0 all V2g_2E0 all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0))),s(A_27a,V3x_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Ebool_2ECOND__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 318 (exists V0f_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0)))))) # label(thm_2Ebool_2EINFINITY__AX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 319 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f165_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,f165_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef165_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 320 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f72_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f72_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef72_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 321 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f70_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f70_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef70_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 322 (all A_27a ((all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0)))) & (all V2t1_2E0 all V3t2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = s(A_27a,V3t2_2E0)))) # label(thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 323 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),f122_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f122_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef122_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 324 (all A_27a all A_27b all A_27c all V1N_2E0 all V0b_2E0 all V4x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V4x_2E0))),s(A_27b,V0b_2E0))) = s(A_27c,f166_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 325 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2Ebool_2Eliteral__case__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 326 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 327 (all A_27a all V1x_27_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f29_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 328 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 329 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_0_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_1_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_3_2E0)))) -> (all V5f_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V5f_2E0))))))) # label(thm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 330 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(thm_2Ebool_2EEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 331 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) -> (all V1i_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),V1i_2E0))))))) # label(thm_2Ebool_2Eitself__induction) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 332 (all V0P_2E0 all V1Q_2E0 all V2R_2E0 ((p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,V2R_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))) & (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))))) # label(thm_2Ebool_2EIMP__CONJ__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 333 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f168_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f168_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef168_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 334 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f30_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f30_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef30_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 335 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONTO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 336 (all A_27a all V0b_2E0 all V1t_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0))) = s(A_27a,V1t_2E0)) # label(thm_2Ebool_2Ebool__case__ID) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 337 (all A_27a all A_27b all V0P_2E0 all V1N_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,f121_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0)))))) # label(def0_2Ethm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 338 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) <-> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0))))) | (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 339 (all V0t_2E0 -(-p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2ENOT__AND) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 340 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))))) # label(thm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 341 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 342 (all A_27a all V0P_2E0 all V1a_2E0 ((exists V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1a_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))))) # label(thm_2Ebool_2EUNWIND__THM1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 343 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 344 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f72_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f72_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef72_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 345 (all A_27a all V0a_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,f144_0_2E2(s(A_27a,V0a_2E0),s(A_27a,V1x_2E0)))) <-> s(A_27a,V1x_2E0) = s(A_27a,V0a_2E0))) # label(def0_2Ethm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 346 (all V0Q_2E0 all V1P_2E0 (((p(s(tyop_2Emin_2Ebool,V1P_2E0)) -> p(s(tyop_2Emin_2Ebool,V0Q_2E0))) -> p(s(tyop_2Emin_2Ebool,V1P_2E0))) -> p(s(tyop_2Emin_2Ebool,V1P_2E0)))) # label(thm_2Ebool_2EPEIRCE) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 347 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 (s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1P_27_2E0) & (p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V2Q_2E0) = s(tyop_2Emin_2Ebool,V3Q_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) & p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2Q_2E0)) & p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2ELEFT__AND__CONG) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 348 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_1_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,f163_1_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_1_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 349 (all V0A_2E0 all V1B_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) | -p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> -(p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)))) & (-(p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0A_2E0)) & -p(s(tyop_2Emin_2Ebool,V1B_2E0))))) # label(thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 350 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) | p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EOR__INTRO__THM2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 351 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 352 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 353 (all V0c_2E0 all V1x_2E0 all V2x_27_2E0 all V3y_2E0 all V4y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> (p(s(tyop_2Emin_2Ebool,V4y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_2E0)))) & (p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0))))))) # label(thm_2EConseqConv_2EIMP__CONG__cond) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 354 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 355 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.85 356 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) & (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 357 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 358 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) & (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) & p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_27_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 359 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 360 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 361 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 362 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 363 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2EConseqConv_2Etrue__imp) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 364 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 365 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 366 (all V0c_2E0 all V1x_2E0 all V2x_27_2E0 all V3y_2E0 all V4y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V2x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))) & (p(s(tyop_2Emin_2Ebool,V4y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0))))))) # label(thm_2EConseqConv_2EIMP__CONG__cond__simple) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 367 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 368 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2s_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0)))) -> ((all V4s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0))))) <-> (all V3s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0)))))))) # label(thm_2EConseqConv_2Eforall__eq__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 369 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EIMP__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 370 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 371 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 372 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 373 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 374 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2EConseqConv_2EASM__MARKER_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2EConseqConv_2EASM__MARKER_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 375 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EIMP__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 376 (all V0x_2E0 all V1x_27_2E0 s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Emin_2Ebool,V1x_27_2E0))) = s(tyop_2Emin_2Ebool,V1x_27_2E0)) # label(thm_2EConseqConv_2EASM__MARKER__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 377 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 378 (all V0c_2E0 all V1x_2E0 ((-p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__TT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 379 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 380 (all A_27a all V0b_2E0 all V1t_2E0 s(A_27a,V1t_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0)))) # label(thm_2EConseqConv_2ECOND__CLAUSES__ID) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 381 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) | p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,V2y_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__disj__strengthen) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 382 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) & (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) -> ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0))) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 383 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) & (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0))) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 384 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 385 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)))) -> ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 386 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 387 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 388 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 389 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2EConseqConv_2EIMP__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 390 (all V0y_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,V1x_2E0) = s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0y_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))) # label(thm_2EConseqConv_2EASM__MARKER__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 391 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 392 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2EConseqConv_2EIMP__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 393 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 394 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 395 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2Efalse__imp) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 396 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2s_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0)))) -> ((exists V4s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0))))) <-> (exists V3s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0)))))))) # label(thm_2EConseqConv_2Eexists__eq__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 397 (all V0c_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__FT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 398 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) | p(s(tyop_2Emin_2Ebool,V3y_27_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__disj__weaken) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 399 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2EConseqConv_2EIMP__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 400 (all V0c_2E0 all V1x_2E0 (-p(s(tyop_2Emin_2Ebool,V0c_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__TF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 401 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 402 (all A_27a all V0t1_2E0 all V1t2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V1t2_2E0)) # label(thm_2EConseqConv_2ECOND__CLAUSES__CF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 403 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 404 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 405 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 406 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 407 (all V0c_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0c_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_2E0)))) # label(thm_2EConseqConv_2ECOND__CLAUSES__FF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 408 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 409 (all A_27a all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0)))) # label(thm_2EConseqConv_2ECOND__CLAUSES__CT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 410 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 411 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 412 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 413 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) & (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) & p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)) & p(s(tyop_2Emin_2Ebool,V0x_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 414 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2ENOT__CLAUSES__X) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 415 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 416 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 417 (all V0lab_2E0 all V1argument_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2E_3A_2D_2E2(s(tyop_2Emin_2Eind,V0lab_2E0),s(tyop_2Emin_2Ebool,V1argument_2E0))) = s(tyop_2Emin_2Ebool,V1argument_2E0)) # label(thm_2Emarker_2Elabel__def) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 418 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 419 (all A_27a all V0x_2E0 s(A_27a,c_2Emarker_2Eunint_2E1(s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Emarker_2Eunint__def) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 420 (all V0b1_2E0 all V1b2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emarker_2EAC_2E2(s(tyop_2Emin_2Ebool,V0b1_2E0),s(tyop_2Emin_2Ebool,V1b2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1b2_2E0)) & p(s(tyop_2Emin_2Ebool,V0b1_2E0)))) # label(thm_2Emarker_2EAC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 421 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emarker_2EAC_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Emarker_2EAC_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Emarker_2EAC_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 422 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 423 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emarker_2E_3A_2D_2E0),s(tyop_2Emin_2Eind,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Emarker_2E_3A_2D_2E2(s(tyop_2Emin_2Eind,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Emarker_2E_3A_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 424 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2EAbbrev_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 425 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 426 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 427 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 428 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 429 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 430 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,V0p_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))))) # label(thm_2Emarker_2Emove__left__conj) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 431 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))))) # label(thm_2Emarker_2Emove__right__disj) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 432 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 433 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 434 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2Estmarker_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 435 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 436 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Emarker_2Estmarker_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Emarker_2Estmarker__def) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 437 (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E1(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Emarker_2EAbbrev__def) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 438 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Emarker_2Emove__right__conj) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 439 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 440 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Emarker_2Eunint_2E0),s(A_27a,X0_2E0))) = s(A_27a,c_2Emarker_2Eunint_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Eunint_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 441 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 442 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 443 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 444 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 445 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 446 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 447 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))))) # label(thm_2Emarker_2Emove__left__disj) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 448 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2ECong_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2ECong_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2ECong_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 449 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 450 (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,c_2Emarker_2ECong_2E1(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Emarker_2ECong__def) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 451 (all A_27a all X0_2E0 s(A_27a,c_2Emarker_2Estmarker_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Emarker_2Estmarker_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 452 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(thm_2EnormalForms_2EEXT__POINT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 453 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27a)),c_2EnormalForms_2EEXT__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2EnormalForms_2EEXT__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 454 (all A_27a all V0p_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,c_2EnormalForms_2EUNIV__POINT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))))))) # label(thm_2EnormalForms_2EUNIV__POINT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.86 455 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 456 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 457 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 458 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 459 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 460 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 461 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 462 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 463 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 464 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,c_2EnormalForms_2EUNIV__POINT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))))) -> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2EnormalForms_2EUNIV__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 465 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 466 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 467 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 468 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 469 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 470 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2EnormalForms_2EEXT__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 471 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 472 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 473 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2EnormalForms_2EUNIV__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,c_2EnormalForms_2EUNIV__POINT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2EnormalForms_2EUNIV__POINT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 474 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 475 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 476 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 477 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 478 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 479 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 480 (all V0s_2E0 all V1r_2E0 all V2q_2E0 all V3p_2E0 (s(tyop_2Emin_2Ebool,V3p_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2q_2E0),s(tyop_2Emin_2Ebool,V1r_2E0),s(tyop_2Emin_2Ebool,V0s_2E0))) <-> (-p(s(tyop_2Emin_2Ebool,V2q_2E0)) | -p(s(tyop_2Emin_2Ebool,V1r_2E0)) | p(s(tyop_2Emin_2Ebool,V3p_2E0))) & (-p(s(tyop_2Emin_2Ebool,V3p_2E0)) | p(s(tyop_2Emin_2Ebool,V0s_2E0)) | p(s(tyop_2Emin_2Ebool,V2q_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2q_2E0)) | p(s(tyop_2Emin_2Ebool,V1r_2E0)) | -p(s(tyop_2Emin_2Ebool,V3p_2E0))) & (p(s(tyop_2Emin_2Ebool,V3p_2E0)) | -p(s(tyop_2Emin_2Ebool,V1r_2E0)) | -p(s(tyop_2Emin_2Ebool,V0s_2E0))) & (p(s(tyop_2Emin_2Ebool,V3p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0s_2E0)) | p(s(tyop_2Emin_2Ebool,V2q_2E0))))) # label(thm_2Esat_2Edc__cond) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 481 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 482 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 483 (all V0A_2E0 all V1B_2E0 all V2C_2E0 ((p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)) -> p(s(tyop_2Emin_2Ebool,V2C_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1B_2E0)) -> p(s(tyop_2Emin_2Ebool,V2C_2E0)))))) # label(thm_2Esat_2EAND__IMP) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 484 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 485 (all V0A_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 486 (all V0B_2E0 all V1A_2E0 (((p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> (-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 487 (all V0q_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,V1p_2E0)) & p(s(tyop_2Emin_2Ebool,V0q_2E0)) -> p(s(tyop_2Emin_2Ebool,V0q_2E0)))) # label(thm_2Esat_2Epth__an2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 488 (all V0q_2E0 all V1p_2E0 ((-p(s(tyop_2Emin_2Ebool,V0q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1p_2E0))) <-> (-p(s(tyop_2Emin_2Ebool,V1p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0q_2E0))) & (p(s(tyop_2Emin_2Ebool,V1p_2E0)) | p(s(tyop_2Emin_2Ebool,V0q_2E0))))) # label(thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 489 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 490 (all V0q_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,V0q_2E0)) & p(s(tyop_2Emin_2Ebool,V1p_2E0)) -> p(s(tyop_2Emin_2Ebool,V1p_2E0)))) # label(thm_2Esat_2Epth__an1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 491 (all V0A_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Esat_2ENOT__ELIM2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 492 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 493 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 494 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 495 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 496 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 497 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 498 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 499 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 500 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V1p_2E0)) -> p(s(tyop_2Emin_2Ebool,V0q_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0q_2E0)))) # label(thm_2Esat_2Epth__ni2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 501 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 502 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V1p_2E0)) | p(s(tyop_2Emin_2Ebool,V0q_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0q_2E0)))) # label(thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 503 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 504 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) <-> (s(tyop_2Emin_2Ebool,V0r_2E0) = s(tyop_2Emin_2Ebool,V1q_2E0) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 505 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V0q_2E0)) | p(s(tyop_2Emin_2Ebool,V1p_2E0))) -> -p(s(tyop_2Emin_2Ebool,V1p_2E0)))) # label(thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 506 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 507 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 508 (all V0p_2E0 (--p(s(tyop_2Emin_2Ebool,V0p_2E0)) -> p(s(tyop_2Emin_2Ebool,V0p_2E0)))) # label(thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 509 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 510 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V1p_2E0)) -> p(s(tyop_2Emin_2Ebool,V0q_2E0))) -> p(s(tyop_2Emin_2Ebool,V1p_2E0)))) # label(thm_2Esat_2Epth__ni1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 511 (all V0A_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) & -p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Esat_2EAND__INV) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 512 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0b_2E0))) # label(thm_2Esat_2EEQT__Imp1) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 513 (all V0B_2E0 all V1A_2E0 ((-p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> (-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EOR__DUAL) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 514 (all V0B_2E0 all V1A_2E0 ((-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | -p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 515 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 516 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 517 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) <-> ((p(s(tyop_2Emin_2Ebool,V1q_2E0)) -> p(s(tyop_2Emin_2Ebool,V0r_2E0))) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 518 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V2p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0r_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 519 (all V0A_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 520 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 521 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 522 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 523 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0)))) # label(thm_2Ecombin_2Eo__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 524 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)),c_2Ecombin_2EFCOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 525 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 526 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(A_27a,X0_2E0))) = s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 527 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ELEFT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 528 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 529 (all A_27a all A_27b all V0f_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))) & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 530 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0)))) <-> (all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0))),s(A_27b,V2x_2E0))) = s(A_27b,V2x_2E0)))) # label(thm_2Ecombin_2ELEFT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 531 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 532 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),f278_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f278_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef278_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 533 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 534 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 535 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 536 (all A_27d all A_27e all A_27f all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.71/19.87 537 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 538 (all A_27a all A_27c all V1f_2E0 all V3x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V3x_2E0))) = s(A_27c,f276_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 539 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))) = s(A_27b,V2b_2E0) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2Ecombin_2EUPDATE__APPLY__ID) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 540 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) <-> (all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0)))))))) # label(thm_2Ecombin_2EASSOC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 541 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2a_2E0 (s(A_27b,V1b_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2a_2E0))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) # label(thm_2Ecombin_2EUPDATE__APPLY__IMP__ID) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 542 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 543 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27d,c_2Ecombin_2EUPDATE_2E4(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27c,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27c,X3_2E0)))) # label(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 544 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 545 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2a_2E0 all V3b_2E0 all V4c_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V4c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))) -> (all V5v_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0)))) & s(A_27b,V4c_2E0) = s(A_27b,V3b_2E0))) # label(thm_2Ecombin_2EUPD__SAME__KEY__UNWIND) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 546 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 all V4d_2E0 (s(A_27a,V1a_2E0) != s(A_27a,V2b_2E0) & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) & s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) | s(A_27a,V1a_2E0) = s(A_27a,V2b_2E0) & s(A_27b,V4d_2E0) = s(A_27b,V3c_2E0) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) # label(thm_2Ecombin_2EUPD11__SAME__BASE) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 547 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))) = s(A_27a,c_2Ecombin_2E_3A_3E_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))) # label(thm_2Ecombin_2EAPP__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 548 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),f279_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f279_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef279_0_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 549 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 all V4d_2E0 (s(A_27a,V2b_2E0) != s(A_27a,V1a_2E0) -> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))))) # label(thm_2Ecombin_2EUPDATE__COMMUTES) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 550 (all A_27a all V1a_2E0 all V3c_2E0 (p(s(tyop_2Emin_2Ebool,f286_0_2E2(s(A_27a,V1a_2E0),s(A_27a,V3c_2E0)))) <-> s(A_27a,V1a_2E0) = s(A_27a,V3c_2E0))) # label(def0_2Ethm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 551 (all A_27a all A_27b all A_27c all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),f278_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 552 (all A_27a s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0)) # label(thm_2Ecombin_2EI__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 553 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 554 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EFAIL_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) = s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 555 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27b,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 556 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 557 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 558 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 all V2y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0)))))) # label(thm_2Ecombin_2ECOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 559 (all A_27a all V0v_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,V0v_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ecombin_2ELET__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 560 (all A_27a all A_27b all A_27c all A_27d ((all V3a_2E0 all V4b_2E0 all V5x_2E0 all V6f_2E0 (s(A_27c,V4b_2E0) != s(A_27c,V3a_2E0) -> s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))) = s(A_27d,c_2Ecombin_2EUPDATE_2E4(s(A_27c,V3a_2E0),s(A_27d,V5x_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))))) & (all V0a_2E0 all V1x_2E0 all V2f_2E0 s(A_27b,V1x_2E0) = s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0a_2E0)))))) # label(thm_2Ecombin_2EUPDATE__APPLY) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 561 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),f279_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 562 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 563 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)) # label(thm_2Ecombin_2EAPPLY__UPDATE__ID) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 564 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 565 (all A_27a all A_27c all V0g_2E0 all V3x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0))) = s(A_27c,f279_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 566 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 567 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f278_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 568 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f278_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f278_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0)))) # label(arityeq1_2Ef278_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.71/19.88 569 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 570 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f279_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27c,f279_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef279_0_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 571 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2h_2E0 s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),V2h_2E0)))) # label(thm_2Ecombin_2Eo__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 572 (all A_27a all V0f_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))))) # label(thm_2Ecombin_2EMONOID__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 573 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 574 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 (s(A_27b,V2b_2E0) = s(A_27b,V3c_2E0) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) # label(thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 575 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 576 (all A_27a all A_27b all A_27c all V0x_2E0 all V1v_2E0 all V2f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1v_2E0))),s(A_27c,V0x_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27c,V0x_2E0))),s(A_27b,V1v_2E0)))) # label(thm_2Ecombin_2EGEN__LET__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 577 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 578 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 579 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 580 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(A_27a,V1x_2E0)) # label(thm_2Ecombin_2EFAIL__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 581 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0)))) <-> (all V2x_2E0 all V3y_2E0 all V4z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0),s(A_27c,V2x_2E0))),s(A_27a,V3y_2E0))))),s(A_27b,V4z_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0),s(A_27c,V2x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,V4z_2E0)))))))) # label(thm_2Ecombin_2EFCOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 582 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 583 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 584 (all A_27a all V0f_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) # label(thm_2Ecombin_2EFCOMM__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 585 (all A_27a all V0f_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))))) # label(thm_2Ecombin_2EASSOC__SYM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 586 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 587 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))),s(A_27b,X2_2E0))) = s(A_27c,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 588 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 589 (all A_27a all A_27b all A_27c all V0v_2E0 all V1f_2E0 all V2P_2E0 s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(A_27c,V0v_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_2E0)))))) # label(thm_2Ecombin_2EGEN__literal__case__RAND) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 590 (all A_27d all A_27f all X0_2E0 s(tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E1(s(A_27d,X0_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27f,A_27d)),c_2Ecombin_2EK_2E0),s(A_27d,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27d_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 591 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 592 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0)))) # label(thm_2Ecombin_2EFAIL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 593 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 594 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27c,X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27c,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 595 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 596 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f286_0_2E2(s(A_27a,V1a_2E0),s(A_27a,V3c_2E0))),s(A_27b,V2b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0)))))) # label(thm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 597 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2ERIGHT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 598 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 599 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EMONOID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 600 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),f281_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f281_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef281_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 601 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f281_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f281_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0)))) # label(arityeq1_2Ef281_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 602 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 603 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 604 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 605 (all A_27a all A_27b all A_27c all V0x_2E0 all V1v_2E0 all V2f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1v_2E0))),s(A_27c,V0x_2E0))) = s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27c,V0x_2E0))),s(A_27b,V1v_2E0)))) # label(thm_2Ecombin_2EGEN__literal__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 606 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))))) = s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),f277_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V2x_2E0)))) # label(thm_2Ecombin_2Eo__ABS__R) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 607 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 608 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 609 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 610 (all A_27a all A_27c all V0g_2E0 all V3x_2E0 s(A_27c,f277_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2Eo__ABS__R) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 611 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0),s(A_27c,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))),s(A_27c,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.88 612 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1f1_2E0 all V2f2_2E0 all V3a_2E0 all V4b_2E0 all V5c_2E0 (s(A_27d,V5c_2E0) != s(A_27d,V4b_2E0) -> s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V4b_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))) != s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V5c_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))))) # label(thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 613 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 614 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0)))) # label(thm_2Ecombin_2EW__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 615 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 616 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27b,V1x_2E0),s(A_27a,V2y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27b,V1x_2E0)))) # label(thm_2Ecombin_2EC__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 617 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))) # label(thm_2Ecombin_2EK__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 618 (all A_27a all A_27b all A_27c all V0v_2E0 all V1f_2E0 all V2P_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_2E0))))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(A_27c,V0v_2E0)))) # label(thm_2Ecombin_2EGEN__LET__RAND) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 619 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 620 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 621 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0)))) # label(thm_2Ecombin_2EK__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 622 (all A_27a all A_27b all A_27c all V0y_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f281_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27c,V0y_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,V0y_2E0)))) # label(thm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 623 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f266_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f266_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef266_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 624 (all A_27e all A_27f all X0_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,A_27e)),c_2Ecombin_2EK_2E0),s(A_27e,X0_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 625 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) # label(thm_2Ecombin_2EUPDATE__EQ) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 626 (all A_27a all V0a_2E0 all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,f266_0_2E2(s(A_27a,V0a_2E0),s(A_27a,V3x_27_2E0)))) <-> s(A_27a,V0a_2E0) = s(A_27a,V3x_27_2E0))) # label(def0_2Ethm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 627 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 628 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X0_2E0) = s(A_27a,X1_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 629 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0x_2E0),s(A_27a,V1x_27_2E0))),s(A_27a,V1x_27_2E0))) = s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2Ecombin_2EW__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 630 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f276_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f276_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef276_0_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 631 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 632 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 633 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,X1_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 634 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 635 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,f276_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f276_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef276_0_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 636 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Ecombin_2EI__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 637 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f ((all V0f_2E0 all V1v_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) & (all V2f_2E0 all V3v_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V2f_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E1(s(A_27d,V3v_2E0))))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V2f_2E0),s(A_27d,V3v_2E0)))))))) # label(thm_2Ecombin_2EK__o__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 638 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 639 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 640 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 641 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 642 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 643 (all A_27a all A_27b all A_27c all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_2E0)))))) # label(thm_2Ecombin_2ES__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 644 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 645 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2x_2E0 all V3x_27_2E0 s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f266_0_2E2(s(A_27a,V0a_2E0),s(A_27a,V3x_27_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0)))))) # label(thm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 646 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 647 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f277_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f277_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef277_0_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 648 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Ecombin_2E_3A_3E_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(A_27a,c_2Ecombin_2E_3A_3E_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2E_3A_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 649 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ERIGHT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 650 (all A_27a all A_27b all A_27c all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27b,V1x_27_2E0),s(A_27a,V2x_27_27_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,V1x_27_2E0)))) # label(thm_2Ecombin_2EC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 651 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2EMONOID_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 652 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 653 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 654 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 ((all V2x_2E0 s(A_27a,V2x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V1e_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27b,V1e_2E0)))))) # label(thm_2Ecombin_2ERIGHT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 655 (all A_27a all A_27b all A_27c all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),f281_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 656 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 657 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f277_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27c,f277_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef277_0_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 658 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V2x_2E0))))) = s(A_27c,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),f276_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V2x_2E0)))) # label(thm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 659 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ELEFT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 660 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 661 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f286_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f286_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef286_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 662 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 663 (all A_27a all V0v_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,V0v_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0)))) # label(thm_2Ecombin_2Eliteral__case__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 664 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 665 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Ecombin_2ES__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 666 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(A_27c,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(A_27c,V2x_2E0)))))) # label(thm_2Ecombin_2Eo__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 667 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)),c_2Ecombin_2EFCOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 668 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 669 (all X0_2E0 s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,X0_2E0))) = s(tyop_2Emin_2Eind,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),c_2Enum_2ESUC__REP_2E0),s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC__REP_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 670 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 671 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,V0m_2E0)))) <-> (all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,c_2Enum_2EZERO__REP_2E0)))) & (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,V2n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,V0m_2E0)))))))) # label(thm_2Enum_2EIS__NUM__REP) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 672 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 673 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 674 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 675 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 676 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 677 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 678 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 679 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) -> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Enum_2EINV__SUC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 680 (all X0_2E0 s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Eind,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),c_2Enum_2EREP__num_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EREP__num_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 681 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 682 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V1n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) -> (all V2n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Enum_2EINDUCTION) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 683 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 684 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 685 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 686 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 687 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 688 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),c_2Enum_2EIS__NUM__REP_2E0),s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EIS__NUM__REP_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 689 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enum_2ENOT__SUC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 690 (all V0y_2E0 s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,V0y_2E0))) != s(tyop_2Emin_2Eind,c_2Enum_2EZERO__REP_2E0)) # label(thm_2Enum_2EZERO__REP__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 691 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 692 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,V0a_2E0))))) = s(tyop_2Enum_2Enum,V0a_2E0)) # label(thm_2Enum_2Enum__ISO__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 693 (all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,V1r_2E0)))) <-> s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,V1r_2E0))))) = s(tyop_2Emin_2Eind,V1r_2E0))) # label(thm_2Enum_2Enum__ISO__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 694 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 695 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 696 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 697 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Enum_2ESUC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 698 (exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),c_2Enum_2EIS__NUM__REP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),V0rep_2E0))))) # label(thm_2Enum_2Enum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.89 699 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Enum_2Enum),c_2Enum_2EABS__num_2E0),s(tyop_2Emin_2Eind,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EABS__num_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 700 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 701 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 702 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONTO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 703 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 704 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 705 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 706 (all A_27a all V0x_2E0 s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Eone_2Eone__case__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 707 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 708 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 709 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 710 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 711 (all V0x_2E0 s(tyop_2Emin_2Ebool,f320_0_2E1(s(tyop_2Eone_2Eone,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(def0_2Ethm_2Eone_2Eone__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 712 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(A_27a,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Eone_2Eone__CASE_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Eone_2Eone__CASE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 713 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 714 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 715 (all X0_2E0 s(tyop_2Emin_2Ebool,f320_0_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),f320_0_2E0),s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ef320_0_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 716 (all X0_2E0 s(tyop_2Emin_2Ebool,f319_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f319_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef319_0_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 717 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool)),f324_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,f324_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),X1_2E0)))) # label(arityeq2_2Ef324_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 718 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 719 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 720 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),f324_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool)),f324_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef324_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 721 (all A_27a all V0e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),f324_0_2E1(s(A_27a,V0e_2E0))))))) # label(thm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 722 (all V1b_2E0 s(tyop_2Emin_2Ebool,V1b_2E0) = s(tyop_2Emin_2Ebool,f319_0_2E1(s(tyop_2Emin_2Ebool,V1b_2E0)))) # label(def0_2Ethm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 723 (all X0_2E0 s(tyop_2Eone_2Eone,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eone_2Eone,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Eone_2Eone),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 724 (all V0P_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))))) # label(thm_2Eone_2EFORALL__ONE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 725 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 726 (all A_27a all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V0f_2E0)) # label(thm_2Eone_2Eone__axiom) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 727 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 728 (all V0v_2E0 s(tyop_2Eone_2Eone,V0v_2E0) = s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)) # label(thm_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 729 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 730 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 731 (exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f319_0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0rep_2E0))))) # label(thm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 732 (all A_27a all V0u_2E0 all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,V0u_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Eone_2Eone__case__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 733 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 734 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 735 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 736 (all A_27a all V0e_2E0 all V1fn_2E0 (p(s(tyop_2Emin_2Ebool,f324_0_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0)))) <-> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))) = s(A_27a,V0e_2E0))) # label(def0_2Ethm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 737 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 738 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 739 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 740 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 741 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 742 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 743 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))) -> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,V1x_2E0))))))) # label(thm_2Eone_2Eone__induction) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 744 (all A_27a all V0e_2E0 exists V1fn_2E0 s(A_27a,V0e_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))) # label(thm_2Eone_2Eone__prim__rec) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 745 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Etotal__inv__image) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 746 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) <-> (exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))))) # label(thm_2Erelation_2ERDOM__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 747 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Ediag_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ediag_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 748 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 749 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> (exists V3u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3u_2E0),s(A_27a,V2y_2E0)))))))) # label(thm_2Erelation_2ERTC__CASES__RTC__TWICE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 750 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__EQ__WFP) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 751 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Esymmetric__SC__identity) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 752 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1P_2E0 ((all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Erelation_2EWF__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 753 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0))))) # label(thm_2Erelation_2Einv__INVOL) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 754 (all A_27a all V0R_2E0 all V1x_2E0 ((all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2EWFP__RULES) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 755 (all A_27a all V0R_2E0 all V1P_2E0 ((all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 756 (all A_27a all A_27b all A_27c all A_27d all V0R3_2E0 all V1R2_2E0 all V2R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V0R3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V0R3_2E0)))))) # label(thm_2Erelation_2EO__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 757 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Enf_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) <-> (all V2y_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))))) # label(thm_2Erelation_2Enf__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 758 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7x_2E0),s(A_27a,V8y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 759 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))))))) # label(thm_2Erelation_2EALT__equivalence) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 760 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ETC__IDEM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 761 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Einv__EQC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 762 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 763 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) | p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__CASES__TC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 764 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))) # label(thm_2Erelation_2ESC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 765 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWCR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWCR_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 766 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 767 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1y_2E0))),s(A_27a,V2z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2z_2E0))),s(A_27a,V1y_2E0)))) <-> s(A_27a,V2z_2E0) = s(A_27a,V1y_2E0))))) # label(thm_2Erelation_2EWeakOrder__EQ) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 768 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etrichotomous_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etrichotomous_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 769 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Einv__image_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0)))))) # label(thm_2Erelation_2Einv__image__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 770 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))) & (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0)))))))) -> (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6y_2E0)))))))))) # label(thm_2Erelation_2ETC__lifts__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 771 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 772 (all A_27a all A_27b all V0R3_2E0 all V1R2_2E0 all V2R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0)))))) # label(thm_2Erelation_2ERINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 773 (all A_27g all V0Z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))))) # label(thm_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 774 (all A_27a all V0R_2E0 all V1P_2E0 ((all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.90 775 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EWFP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 776 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 777 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Ereflexive__Id__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 778 (all A_27a all V0R_2E0 all V1Q_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2a_2E0)))) & (all V3y_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4z_2E0)))))) -> (all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2a_2E0),s(A_27a,V5z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V5z_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 779 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) -> (exists V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3z_2E0),s(A_27a,V4u_2E0)))))))))) # label(thm_2Erelation_2Ercdiamond__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 780 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2EWFP__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 781 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERCOMPL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERCOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERCOMPL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 782 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) # label(thm_2Erelation_2ESTRORD__RC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 783 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 784 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ESN__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 785 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 786 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0)))) # label(thm_2Erelation_2ERUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 787 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ETC__RC__EQNS) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 788 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2EWFREC_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 789 (all A_27a all A_27b all V0x_2E0 all V1k_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM__DELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1k_2E0)))))))) <-> s(A_27a,V1k_2E0) != s(A_27a,V0x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 790 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ediamond_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ediamond_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 791 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2Ethe__fun_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Erelation_2Ethe__fun_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2Ethe__fun_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 792 (all A_27g all A_27h all A_27k all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EO_2E4(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27g,V2x_2E0),s(A_27k,V3z_2E0)))) <-> (exists V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27g,V2x_2E0))),s(A_27h,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27h,V4y_2E0))),s(A_27k,V3z_2E0)))))))) # label(thm_2Erelation_2EO__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 793 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> (all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V3z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3z_2E0)))))))) # label(thm_2Erelation_2ERTC__RTC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 794 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))))),s(A_27a,V2x_2E0))) = s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Erelation_2EWFREC__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 795 (all A_27a all A_27b all V1M_2E0 all V3f_2E0 all V0R_2E0 all V4y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))))),s(A_27a,V4y_2E0))) = s(A_27b,f346_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0)))) # label(def0_2Ethm_2Erelation_2Eapprox__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 796 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0)))) # label(thm_2Erelation_2ERC__OR__Id) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 797 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 (s(A_27a,V2b_2E0) != s(A_27a,V1a_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESTRORD_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))))) # label(thm_2Erelation_2ESTRORD) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 798 (all A_27a all A_27b all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1M_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f489_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))))) # label(thm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 799 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f347_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),f347_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef347_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 800 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNIV_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 801 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Einv__RC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 802 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 803 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ECR__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 804 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ercdiamond_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ercdiamond_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 805 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 all V2x_2E0 all V3x_27_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Einv__image_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0),s(A_27a,V3x_27_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_27_2E0)))))) # label(thm_2Erelation_2Einv__image__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 806 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 807 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))) # label(thm_2Erelation_2ERSUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 808 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) # label(thm_2Erelation_2ERINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 809 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 810 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eantisymmetric__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 811 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 812 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ERC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 813 (all A_27g all V0Z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))))) # label(thm_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 814 (all A_27a all V0a_2E0 all V1R_2E0 all V2Q_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0a_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V5y_2E0)))))) -> (all V6b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0a_2E0),s(A_27a,V6b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V6b_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__ALT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 815 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERINTER_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERINTER_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 816 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 ((all V3P_2E0 ((all V5x_2E0 all V6y_2E0 all V7z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V6y_2E0))),s(A_27a,V7z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V5x_2E0))),s(A_27a,V7z_2E0)))))) & (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V4x_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))))) # label(thm_2Erelation_2ERTC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 817 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 818 (all A_27z all V0f_2E0 (s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2EI_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EINVOL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 819 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 820 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERDOM__DELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM__DELETE_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERDOM__DELETE_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 821 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Einv__SC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 822 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) | (exists V3u_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3u_2E0))),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3u_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__CASES2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 823 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Erelation_2ERESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERESTRICT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 824 (all A_27a all A_27b all V1M_2E0 all V0R_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,f489_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) <-> (all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))))),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 825 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2EEQC__R) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 826 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 827 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eirrefl__trans__implies__antisym) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 828 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 829 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 830 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))) <-> (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))))))) # label(thm_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 831 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERTC__IDEM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 832 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.91 833 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 834 (all A_27a all V0R_2E0 all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))))) # label(thm_2Erelation_2EEQC__REFL) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 835 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 836 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> (exists V4u_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3z_2E0))),s(A_27a,V4u_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Ediamond__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 837 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 838 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__SINGLE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 839 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f489_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),f489_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef489_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 840 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Einv__TC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 841 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERC__RTC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 842 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 ((all V3P_2E0 ((all V6x_2E0 all V7y_2E0 all V8z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))))) # label(thm_2Erelation_2ETC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 843 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ESC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 844 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0)))) # label(thm_2Erelation_2EWF__NOT__REFL) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 845 (all A_27a all A_27b p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0))))) # label(thm_2Erelation_2ERSUBSET__WeakOrder) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 846 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 847 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 848 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Ereflexive__EQC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 849 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ETC__RTC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 850 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27b,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Einv_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,V1x_2E0),s(A_27a,V2y_2E0)))) # label(thm_2Erelation_2Einv__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 851 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 852 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ETC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 853 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 854 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 855 (all A_27a all V0b_2E0 all V1R_2E0 all V2Q_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V0b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V4x_2E0)))))) -> (all V6a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V6a_2E0),s(A_27a,V0b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V6a_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__ALT__LEFT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 856 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 857 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2u_2E0 all V3v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM__DELETE_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2u_2E0),s(A_27b,V3v_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2u_2E0))),s(A_27b,V3v_2E0)))) & s(A_27a,V2u_2E0) != s(A_27a,V1x_2E0))) # label(thm_2Erelation_2ERDOM__DELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 858 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))))))) # label(thm_2Erelation_2ERTC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 859 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 860 (all A_27a all V0z_2E0 all V1x_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0z_2E0)))) | (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V0z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3y_2E0)))))))) # label(thm_2Erelation_2ETC__CASES2) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 861 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Einv__image_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2Einv__image_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 862 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V3z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3z_2E0)))))) # label(thm_2Erelation_2EEQC__TRANS) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 863 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 864 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Esymmetric__EQC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 865 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) | s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) # label(thm_2Erelation_2ERC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 866 (all A_27z all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool),c_2Erelation_2EIDEM_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EIDEM_2E1_2Emono_2EA_27z) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 867 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 868 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_2E0 all V3D_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3D_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 869 (all A_27a all A_27b all V0M_2E0 all V1R_2E0 all V2f_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V0M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) -> (all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V0M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_2E0))))),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Erelation_2EWFREC__COROLLARY) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 870 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 871 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__TC__RC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 872 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Ereflexive__RC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 873 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))) <-> (all V3Q_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V1a_2E0)))) & (all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V5z_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V2b_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__RIGHT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 874 (all A_27a all V0R_2E0 ((all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2b_2E0))),s(A_27a,V1a_2E0)))) | s(A_27a,V2b_2E0) = s(A_27a,V1a_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 875 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ECR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ECR_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 876 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERRESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERRESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 877 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakLinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 878 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 879 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Erelation_2ERTC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 880 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 881 (all A_27a all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Erelation_2Etransitive__RINTER) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 882 (all A_27a all V0R_2E0 all V1x_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2z_2E0)))) <-> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0),s(A_27a,V2z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3y_2E0)))))))) # label(thm_2Erelation_2EEXTEND__RTC__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 883 (all A_27a all V0R_2E0 all V1Q_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2b_2E0)))) & (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5x_2E0),s(A_27a,V2b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V5x_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.74/19.92 884 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 885 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 886 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1P_2E0 ((all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Erelation_2EWF__EQ__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 887 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ESC__SYMMETRIC) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 888 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))))) & (all V2x_2E0 all V3y_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Erelation_2ERTC__RULES__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 889 (all A_27a all V0R_2E0 all V1P_2E0 ((all V7x_2E0 all V8y_2E0 all V9z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V8y_2E0),s(A_27a,V9z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7x_2E0),s(A_27a,V8y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V8y_2E0))),s(A_27a,V9z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V9z_2E0)))))) & (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5x_2E0)))))) & (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V4x_2E0))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V10x_2E0 all V11y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V10x_2E0),s(A_27a,V11y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V10x_2E0))),s(A_27a,V11y_2E0)))))))) # label(thm_2Erelation_2ESTRONG__EQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 890 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERRANGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 891 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EEQC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EEQC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 892 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)))),f346_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),f346_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0)))) # label(arityeq3_2Ef346_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 893 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ESC__IDEM) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 894 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 895 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) -> (exists V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3z_2E0),s(A_27a,V4u_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWCR__def) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 896 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.74/19.93 897 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2D_2E0 all V3P_2E0 all V4M_2E0 all V5x_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V4M_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2D_2E0),s(A_27a,V5x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V4M_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0)))))))) # label(thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 898 (all A_27a all A_27b all V0R3_2E0 all V1R2_2E0 all V2R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0)))) # label(thm_2Erelation_2ERUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 899 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Erelation_2EINVOL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 900 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERCOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERCOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERCOMPL_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 901 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 902 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Esymmetric__def) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 903 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 904 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 905 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 906 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) # label(thm_2Erelation_2Eequivalence__inv__identity) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 907 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2EEQC__MOVES__IN) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 908 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Etransitive__RTC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 909 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 910 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Erelation_2ETC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 911 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0))))) # label(thm_2Erelation_2EWF__EMPTY__REL) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 912 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2Ethe__fun_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f347_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 913 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 914 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 915 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) & (all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 916 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERTC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 917 (all A_27g all V0Z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))))) # label(thm_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 918 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),f348_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f348_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef348_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 919 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 920 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 921 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EWF__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 922 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Erelation_2ERC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 923 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0))))) # label(thm_2Erelation_2EIDEM__STRORD) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 924 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EEQC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 925 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) & (all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 926 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Esymmetric__inv__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 927 (all A_27a all A_27b all V0y_2E0 all V1z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0y_2E0))) # label(thm_2Erelation_2EEqIsBothRSUBSET) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 928 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERC__IDEM) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 929 (all A_27z all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool),c_2Erelation_2EINVOL_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2EA_27z) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 930 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 931 (all A_27a all V0A_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0)))) # label(thm_2Erelation_2Einv__diag) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 932 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))) # label(thm_2Erelation_2ETC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 933 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)))),c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 934 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 935 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2Ethe__fun_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f348_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))))),s(A_27a,V2x_2E0))) = s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0)))) # label(thm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 936 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.93 937 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 938 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2P_2E0 all V3M_2E0 all V4x_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 939 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ETC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 940 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ERC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 941 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Ereflexive__RC__identity) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 942 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> s(A_27a,V0y_2E0) != s(A_27a,V1x_2E0)))) # label(thm_2Erelation_2EWF__noloops) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 943 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ERTC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 944 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Etrichotomous__RC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 945 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V3z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3z_2E0)))))) # label(thm_2Erelation_2EEXTEND__RTC__TC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 946 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2EEQC__EQUIVALENCE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 947 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 948 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Erelation_2EIDEM_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EIDEM_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 949 (all A_27a all A_27b all V0y_2E0 all V1R_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27b,V2x_2E0))),s(A_27a,V0y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))))))) # label(thm_2Erelation_2EIN__RRANGE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 950 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERCOMPL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27b,V2y_2E0)))))) # label(thm_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 951 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ETC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 952 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 953 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EEQC__IDEM) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 954 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 955 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ESC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 956 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 957 (all A_27a all V0x_2E0 all V1R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0x_2E0),s(A_27a,V0x_2E0))))) # label(thm_2Erelation_2ERTC__REFL) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 958 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Ereflexive__TC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 959 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eequivalence_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eequivalence_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 960 (all A_27a all A_27b all A_27c all V0S2_2E0 all V1S1_2E0 all V2R2_2E0 all V3R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1S1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0S2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1S1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0S2_2E0)))))))) # label(thm_2Erelation_2EO__MONO) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 961 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 962 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))) <-> (all V3Q_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V2b_2E0)))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V4x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V1a_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 963 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EId__O) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 964 (all A_27a all A_27b all V1M_2E0 all V0R_2E0 all V3f_2E0 all V4v_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4v_2E0))))),s(A_27a,V4v_2E0))) = s(A_27b,f348_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4v_2E0)))) # label(def0_2Ethm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 965 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2Q_2E0 ((all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))) -> (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6y_2E0)))))))))) # label(thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 966 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EStrongOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 967 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Ereflexive__RTC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 968 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 969 (all A_27a all V0A_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediag_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2Ediag__def) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 970 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 all V3f_2E0 s(tyop_2Emin_2Ebool,f347_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eapprox_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0)))) # label(def0_2Ethm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 971 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) & s(A_27a,V1x_2E0) != s(A_27a,V3z_2E0))))) # label(thm_2Erelation_2ETC__implies__one__step) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 972 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERRESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERRESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERRESTRICT_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 973 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))))))) # label(thm_2Erelation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 974 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 975 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2EEQC__SYM) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 976 (all A_27z all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))) -> (all V1a_2E0 all V2b_2E0 (s(A_27z,V1a_2E0) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V2b_2E0))) <-> s(A_27z,V2b_2E0) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1a_2E0))))))) # label(thm_2Erelation_2EINVOL__ONE__ENO) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 977 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27b,c_2Erelation_2ERESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))))) # label(thm_2Erelation_2ERESTRICT__LEMMA) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 978 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Etransitive__TC__identity) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 979 (all A_27a all A_27b all V0R_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERRANGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,V1y_2E0)))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27b,V1y_2E0))))))) # label(thm_2Erelation_2ERRANGE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 980 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__EQC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 981 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EEMPTY__REL_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EEMPTY__REL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 982 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 983 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERC__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 984 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Etransitive__inv) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 985 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ESC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 986 (all A_27z all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))) -> (all V1a_2E0 all V2b_2E0 (s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1a_2E0))) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V2b_2E0))) <-> s(A_27z,V2b_2E0) = s(A_27z,V1a_2E0))))) # label(thm_2Erelation_2EINVOL__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 987 (all A_27z all V0f_2E0 (s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0) = s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EIDEM__DEF) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 988 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Erelation_2ERESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(A_27b,c_2Erelation_2ERESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERESTRICT_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 989 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERRANGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERRANGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERRANGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 990 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 991 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ERTC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 992 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 993 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 994 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Esymmetric__TC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 995 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0))))) # label(thm_2Erelation_2EIDEM__RC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 996 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0)))) -> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0),s(A_27a,V3x_2E0))))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 997 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 998 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 999 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eequivalence__def) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 1000 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,f348_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),f348_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef348_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.78/19.94 1001 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.94 1002 (all A_27a all V0R_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0)))))) # label(thm_2Erelation_2EWF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 19.81/19.94 1003 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eantisymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 19.81/19.94 1004 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Ereflexive__inv__image) # label(axiom) # label(non_clause). [assumption]. 19.81/19.94 1005 (all A_27a all V0R1_2E0 all V1R2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0)))))) # label(thm_2Erelation_2Eirreflexive__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 19.81/19.94 1006 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f489_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),f489_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ef489_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1007 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1008 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1009 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Ercdiamond__diamond) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1010 (all A_27a all A_27b all A_27c all V0R_2E0 all V1R_27_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_27_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_27_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Einv__O) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1011 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Ediamond__TC__diamond) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1012 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1013 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Ereflexive__inv) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1014 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7x_2E0),s(A_27a,V8y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1015 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Enf_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Enf_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2Enf_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1016 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) # label(thm_2Erelation_2Esymmetric__inv__identity) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1017 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2x_2E0 all V3x_27_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_27_2E0))),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_27_2E0))),s(A_27b,c_2Ebool_2EARB_2E0))) = s(A_27b,c_2Erelation_2ERESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0),s(A_27a,V3x_27_2E0)))) # label(thm_2Erelation_2ERESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1018 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1019 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Eantisymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1020 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)) # label(thm_2Erelation_2Einv__inv) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1021 (all A_27a all V0R2_2E0 all V1R1_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0))))))))) # label(thm_2Erelation_2Eantisymmetric__RINTER) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1022 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_27_2E0 all V3R_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_27_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2EEQC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1023 (all A_27a all V0R_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) <-> (all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0)))))))) # label(thm_2Erelation_2EWFP__CASES) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1024 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Einv_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2Einv_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1025 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1026 (all A_27g all A_27h all A_27k all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EO_2E4(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X1_2E0),s(A_27g,X2_2E0),s(A_27k,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27g,X2_2E0))),s(A_27k,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2EO_2E4_2Emono_2EA_27g_20mono_2EA_27h_20mono_2EA_27k) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1027 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1028 (all A_27a all V0z_2E0 all V1x_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0z_2E0)))) <-> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3y_2E0),s(A_27a,V0z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3y_2E0)))))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0z_2E0)))))) # label(thm_2Erelation_2ETC__CASES1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1029 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0))))) # label(thm_2Erelation_2EIDEM__RTC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1030 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Ediamond__RC__diamond) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1031 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ENewmans__lemma) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1032 (all A_27a all V0R_2E0 ((all V1P_2E0 ((all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EINDUCTION__WF__THM) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1033 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Erelation_2Eapprox_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eapprox_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2Eapprox_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1034 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERC__STRORD) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1035 (all A_27a all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EEMPTY__REL_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Erelation_2EEMPTY__REL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1036 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERDOM_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1037 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1038 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNION_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERUNION_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1039 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EEQC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2EEQC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1040 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERTC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1041 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0)))))))) # label(thm_2Erelation_2EWF__inv__image) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1042 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERC__Weak) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1043 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1044 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Esymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1045 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1046 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWeakOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1047 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1048 (all A_27a all A_27b all V0x_2E0 all V1R_2E0 ((exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0x_2E0))),s(A_27b,V2y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1049 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1050 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1051 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERDOM__DELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM__DELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERDOM__DELETE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1052 (all A_27a all V0R_2E0 ((all V2x_2E0 all V3y_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0),s(A_27a,V4z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V4z_2E0)))))) & (all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Erelation_2ERTC__RULES) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1053 (all A_27a all A_27b all V0R_2E0 all V1D_2E0 all V2P_2E0 all V3M_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0)))) <-> (all V4f_2E0 all V5x_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(A_27a,V6y_2E0)))) -> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V6y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V6y_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))),s(A_27a,V5x_2E0)))))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1054 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1055 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EREMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1056 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1057 (all A_27a all A_27b all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1058 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EPreOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EPreOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EPreOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1059 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ESTRORD__Strong) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1060 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1061 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Eirreflexive__inv) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1062 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))))))) # label(thm_2Erelation_2Etotal__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1063 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1064 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Etransitive__inv__image) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1065 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ETC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.95 1066 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1067 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ESTRORD_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ESTRORD_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1068 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2ESC__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1069 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1070 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWeakLinearOrder) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1071 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1072 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Einv__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1073 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Erelation_2EINDUCTIVE__INVARIANT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2EINDUCTIVE__INVARIANT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1074 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNION_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(thm_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1075 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNIV_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNIV_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1076 (all A_27a all A_27b p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0))))) # label(thm_2Erelation_2ERSUBSET__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1077 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ELinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1078 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Etrichotomous__STRORD) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1079 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Erelation_2EINVOL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1080 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ESN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1081 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Etransitive__RC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1082 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_2E0 ((all V3f_2E0 all V4x_2E0 ((all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V5y_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0))),s(A_27a,V4x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0)))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1083 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0))))) # label(thm_2Erelation_2EIDEM__TC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1084 (all A_27z all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X1_2E0))) = s(tyop_2Emin_2Efun(A_27z,A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(A_27z,A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(A_27z,A_27z))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0))),s(tyop_2Emin_2Efun(A_27z,A_27z),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27z_20mono_2EA_27z_20mono_2EA_27z) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1085 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2ERINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1086 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1087 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2EWF__TC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1088 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Esymmetric__inv__image) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1089 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V4x_2E0))))) & (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5x_2E0)))))) & (all V7x_2E0 all V8y_2E0 all V9z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V8y_2E0))),s(A_27a,V9z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V9z_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V10x_2E0 all V11y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V10x_2E0),s(A_27a,V11y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V10x_2E0))),s(A_27a,V11y_2E0)))))))) # label(thm_2Erelation_2EEQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1090 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0)))) # label(thm_2Erelation_2Einv__Id) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1091 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1092 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1093 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EPreOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1094 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERINTER_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(thm_2Erelation_2ERINTER) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1095 (all A_27a all V0R_2E0 all V1x_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2z_2E0)))) -> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3y_2E0)))))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2z_2E0)))))) # label(thm_2Erelation_2ETC__CASES2__E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1096 (all A_27a all V0R_2E0 all V1x_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2z_2E0)))) -> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0),s(A_27a,V2z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3y_2E0)))))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2z_2E0)))))) # label(thm_2Erelation_2ETC__CASES1__E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1097 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Etransitive__EQC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1098 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0)))) # label(thm_2Erelation_2EO__Id) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1099 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1100 (all A_27a all A_27b all V0R_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERRESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(thm_2Erelation_2ERRESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1101 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)))),f346_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27a,X3_2E0))) = s(A_27b,f346_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef346_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1102 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERCOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ESTRORD__AND__NOT__Id) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1103 (all A_27a all V0R_2E0 ((all V1B_2E0 ((exists V2w_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V2w_2E0))))) -> (exists V3min_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V3min_2E0)))) & (all V4b_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4b_2E0))),s(A_27a,V3min_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V4b_2E0)))))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1104 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Esymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1105 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 all V3f_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),f346_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eapprox_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0)))))) # label(thm_2Erelation_2Eapprox__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1106 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__irreflexive) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1107 (all A_27a all V0P_2E0 all V1R_2E0 ((all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3y_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2EWFP__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1108 (all A_27z all V0f_2E0 ((all V1x_2E0 s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1x_2E0))))) = s(A_27z,V1x_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1109 (all A_27z all V0f_2E0 ((all V1x_2E0 s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1x_2E0))))) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1110 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1111 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1112 (all A_27a all V0R_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Eestablish__CR) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1113 (all A_27a all A_27b all V0x_2E0 all V1s_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERRESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) # label(thm_2Erelation_2EIN__RDOM__RRESTRICT) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1114 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1115 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2b_2E0))),s(A_27a,V1a_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWeakLinearOrder__dichotomy) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1116 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))) # label(thm_2Erelation_2ERC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1117 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f347_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),f347_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ef347_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1118 (all A_27a all A_27b all V0x_2E0 all V1R2_2E0 all V2R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM__RUNION) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1119 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1120 (all A_27a all V0R_2E0 all V1a_2E0 ((all V2P_2E0 ((all V3x_2E0 ((all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1a_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0)))))) # label(thm_2Erelation_2EWFP__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1121 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESC_2E0))))) # label(thm_2Erelation_2EIDEM__SC) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1122 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Etransitive__O__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1123 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1124 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1125 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) & (all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0),s(A_27a,V5z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V5z_2E0)))))))) # label(thm_2Erelation_2ETC__RULES) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1126 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.96 1127 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ELinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ELinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ELinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1128 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3u_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3u_2E0),s(A_27a,V2y_2E0)))))) | s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__CASES1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1129 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Ediag_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ediag_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2Ediag_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1130 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1131 (all A_27a all A_27b all A_27c all V0sum_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),A_27c)),V0sum_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0))))))) # label(thm_2Esum_2Edatatype__sum) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1132 (all A_27a all A_27b all V0e_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f572_0_2E1(s(A_27a,V0e_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0e_2E0)))) # label(thm_2Esum_2EINL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1133 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1134 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1135 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2h_2E0 (p(s(tyop_2Emin_2Ebool,f585_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0))) & s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0))) # label(def0_2Ethm_2Esum_2Esum__axiom) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1136 (all A_27a all A_27b all A_27c all A_27d ((all V3f_2E0 all V4g_2E0 all V5b_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4g_2E0),s(A_27b,V5b_2E0))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V5b_2E0)))))) & (all V0f_2E0 all V1g_2E0 all V2a_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V2a_2E0))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2a_2E0)))))))) # label(thm_2Esum_2ESUM__MAP__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1137 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1138 (all A_27a all A_27b exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Esum_2EIS__SUM__REP_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0rep_2E0))))) # label(thm_2Esum_2Esum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1139 (all A_27g all A_27h all X0_2E0 s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,X0_2E0))) = s(tyop_2Esum_2Esum(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Esum_2Esum(A_27g,A_27h)),c_2Esum_2EINR_2E0),s(A_27h,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1140 (all A_27g all A_27h all X0_2E0 s(tyop_2Esum_2Esum(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Esum_2Esum(A_27g,A_27h)),c_2Esum_2EINL_2E0),s(A_27g,X0_2E0))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINL_2E1(s(A_27g,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1141 (all A_27e all A_27f all X0_2E0 s(tyop_2Esum_2Esum(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Esum_2Esum(A_27e,A_27f)),c_2Esum_2EINL_2E0),s(A_27e,X0_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINL_2E1(s(A_27e,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1142 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2E_2B_2B_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)))),c_2Esum_2E_2B_2B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1143 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1144 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Esum_2E_2B_2B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2E_2B_2B_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1145 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1146 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1147 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINR_2E1(s(A_27c,X0_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27d,A_27c)),c_2Esum_2EINR_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1148 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Esum_2ENOT__ISL__ISR) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1149 (all A_27a all A_27b all V0e_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,f572_0_2E4(s(A_27a,V0e_2E0),s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))) <-> s(A_27a,V2x_2E0) = s(A_27a,V0e_2E0) & p(s(tyop_2Emin_2Ebool,V1b_2E0)))) # label(def0_2Ethm_2Esum_2EINL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1150 (all A_27a all A_27b all A_27c all V0f1_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4f_2E0 all V5f1_2E0 ((all V7y_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V7y_2E0))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0),s(A_27b,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f1_27_2E0),s(A_27b,V7y_2E0))))) & (all V6x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V6x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(A_27a,V6x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_27_2E0),s(A_27a,V6x_2E0))))) & s(tyop_2Esum_2Esum(A_27a,A_27b),V2M_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) -> s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),V2M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0))) = s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_27_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0f1_27_2E0))))) # label(thm_2Esum_2Esum__case__cong) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1151 (all A_27a all A_27b all V0P_2E0 ((all V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_2E0))))))) & (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0))))))) -> (all V3s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V3s_2E0))))))) # label(thm_2Esum_2Esum__INDUCT) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1152 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1153 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2z_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINL_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0)))) # label(thm_2Esum_2ESUM__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1154 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f572_0_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f572_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef572_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1155 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINL_2E1(s(A_27d,X0_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27d,A_27c)),c_2Esum_2EINL_2E0),s(A_27d,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1156 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X1_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X1_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1157 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1158 (all A_27a all A_27b ((all V2y_2E0 all V3x_2E0 (s(A_27b,V3x_2E0) = s(A_27b,V2y_2E0) <-> s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_2E0))))) & (all V0y_2E0 all V1x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0y_2E0))) <-> s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0))))) # label(thm_2Esum_2EINR__INL__11) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1159 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1160 (all A_27a all A_27b all V0x_2E0 s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1161 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f573_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,f573_0_2E4(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef573_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1162 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1y_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Esum_2Esum__distinct) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1163 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Esum_2Esum__CASE_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1164 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1165 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1166 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f572_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f572_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef572_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1167 (all A_27a all A_27b all V0e_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (-p(s(tyop_2Emin_2Ebool,V1b_2E0)) & s(A_27b,V0e_2E0) = s(A_27b,V3y_2E0) <-> p(s(tyop_2Emin_2Ebool,f573_0_2E4(s(A_27b,V0e_2E0),s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(def0_2Ethm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1168 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1169 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1170 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1171 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Esum_2ESUM__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2ESUM__ALL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1172 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27c,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1173 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool))),f585_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),f585_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0)))) # label(arityeq2_2Ef585_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1174 (all A_27a all A_27b all V0v1_2E0 all V1v2_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1v2_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0v1_2E0)))) # label(thm_2Esum_2Esum__distinct1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1175 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1176 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Esum_2EISL_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1177 (all A_27a all A_27b all V0s_2E0 all V1s_27_2E0 all V2P_2E0 all V3P_27_2E0 all V4Q_2E0 all V5Q_27_2E0 ((all V6a_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V6a_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V6a_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V6a_2E0))))) & (all V7b_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V7b_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(A_27b,V7b_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V7b_2E0))))) & s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0) -> s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0))))) # label(thm_2Esum_2ESUM__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1178 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Esum_2Esum(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Esum_2Esum(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Esum_2Esum(A_27b,A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27b,A_27a),X1_2E0))),s(tyop_2Esum_2Esum(A_27b,A_27a),X2_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),X1_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1179 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1180 (all A_27e all A_27f all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27e,A_27f)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),X1_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),X1_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27e_2CA_27f_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1181 (all A_27a all A_27b all V0e_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0e_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f573_0_2E1(s(A_27b,V0e_2E0)))))) # label(thm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1182 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27d,A_27c),X1_2E0),s(tyop_2Esum_2Esum(A_27d,A_27c),X2_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Esum_2Esum(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Esum_2Esum(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Esum_2Esum(A_27d,A_27c)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27d,A_27c),X1_2E0))),s(tyop_2Esum_2Esum(A_27d,A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27d_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1183 (all A_27a all A_27b all V0ss_2E0 ((exists V1x_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),V0ss_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0)))) | (exists V2y_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V0ss_2E0)))) # label(thm_2Esum_2Esum__CASES) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1184 (all A_27a all A_27b all V0x_2E0 s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0x_2E0))))) = s(A_27b,V0x_2E0)) # label(thm_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1185 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1186 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1187 (all A_27a all A_27b ((all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & (all V3P_2E0 all V4Q_2E0 all V5y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V5y_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V5y_2E0)))))))) # label(thm_2Esum_2ESUM__ALL__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1188 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2z_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0))))))),s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0))))))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0)))) # label(thm_2Esum_2ESUM__MAP) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1189 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1190 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool))),f585_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X2_2E0))) = s(tyop_2Emin_2Ebool,f585_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X2_2E0)))) # label(arityeq3_2Ef585_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1191 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1192 (all A_27g all A_27h all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Esum_2Esum(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Esum_2Esum(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Esum_2Esum(A_27g,A_27h)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27g,A_27h),X1_2E0))),s(tyop_2Esum_2Esum(A_27g,A_27h),X2_2E0))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27g,A_27h),X1_2E0),s(tyop_2Esum_2Esum(A_27g,A_27h),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27g_2CA_27h_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1193 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27a),c_2Esum_2EOUTL_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EOUTL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1194 (all A_27a all A_27b ((all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0x_2E0))))))) & (all V1y_2E0 -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1y_2E0))))))))) # label(thm_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1195 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1196 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Esum_2EIS__SUM__REP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Esum_2EIS__SUM__REP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EIS__SUM__REP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1197 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0y_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0))) <-> s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0))) # label(thm_2Esum_2EINL__11) # label(axiom) # label(non_clause). [assumption]. 19.81/19.97 1198 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),f585_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0))))))) # label(thm_2Esum_2Esum__axiom) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1199 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINL_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINL_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1200 (all A_27a all A_27b all V0P_2E0 ((exists V3y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3y_2E0))))))) | (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))))) <-> (exists V1s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_2E0))))))) # label(thm_2Esum_2EEXISTS__SUM) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1201 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1202 (all A_27a all A_27b ((all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))))))) & (all V1y_2E0 -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1y_2E0))))))))) # label(thm_2Esum_2EISL) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1203 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) -> s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))))) # label(thm_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1204 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2E_2B_2B_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Ecombin_2EI_2E0)) # label(thm_2Esum_2ESUM__MAP__I) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1205 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1206 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EABS__sum_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EABS__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1207 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0y_2E0))) <-> s(A_27b,V1x_2E0) = s(A_27b,V0y_2E0))) # label(thm_2Esum_2EINR__11) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1208 (all A_27a all A_27b ((all V1r_2E0 (s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Esum_2EREP__sum_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1r_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Esum_2EIS__SUM__REP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1r_2E0)))))) & (all V0a_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),V0a_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Esum_2EREP__sum_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0a_2E0)))))))) # label(thm_2Esum_2Esum__ISO__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1209 (all A_27a all A_27b all A_27c ((all V0x_2E0 all V1f_2E0 all V2f1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V0x_2E0))) = s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V2f1_2E0)))) & (all V3y_2E0 all V4f_2E0 all V5f1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0),s(A_27b,V3y_2E0))) = s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0)))))) # label(thm_2Esum_2Esum__case__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1210 (all A_27a all A_27b all V0v1_2E0 all V1v2_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1v2_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0v1_2E0)))) # label(thm_2Esum_2EINR__neq__INL) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1211 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f573_0_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f573_0_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef573_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1212 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Esum_2EISL__OR__ISR) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1213 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 exists V2h_2E0 ((all V3x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V3x_2E0)))))) & (all V4y_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V4y_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(A_27b,V4y_2E0)))))) # label(thm_2Esum_2Esum__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1214 (all A_27a all A_27b all V0s_2E0 all V1Q_27_2E0 all V2Q_2E0 all V3P_27_2E0 all V4P_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(A_27b,V6y_2E0)))))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V5x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0))))))) # label(thm_2Esum_2ESUM__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1215 (all A_27a all A_27b all V0f_2E0 ((exists V1v1_2E0 exists V2v2_2E0 ((all V3x_2E0 all V4x_27_2E0 all V5x_27_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Emin_2Ebool,V3x_2E0))),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))) <-> s(A_27a,V4x_27_2E0) = s(A_27a,V1v1_2E0) & p(s(tyop_2Emin_2Ebool,V3x_2E0)))) | (all V6x_2E0 all V7x_27_2E0 all V8x_27_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Emin_2Ebool,V6x_2E0))),s(A_27a,V7x_27_2E0))),s(A_27b,V8x_27_27_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V6x_2E0)) & s(A_27b,V8x_27_27_2E0) = s(A_27b,V2v2_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Esum_2EIS__SUM__REP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0f_2E0)))))) # label(thm_2Esum_2EIS__SUM__REP) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1216 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Esum_2EREP__sum_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Esum_2EREP__sum_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EREP__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1217 (all A_27a all A_27b all X0_2E0 s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27b),c_2Esum_2EOUTR_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EOUTR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1218 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINR_2E0),s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1219 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1220 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1221 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) -> s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))) # label(thm_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1222 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c))),c_2Esum_2Esum__CASE_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1223 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1224 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Esum_2EISR_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1225 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINL_2E0),s(A_27c,X0_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1226 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f all A_27g all A_27h all V0P_2E0 ((all V10x_2E0 all V11y_2E0 all V12z_2E0 (s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINL_2E1(s(A_27g,V10x_2E0))),s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,V11y_2E0))))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,V12z_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0P_2E0)) & s(A_27h,V11y_2E0) = s(A_27h,V12z_2E0))) & (all V7x_2E0 all V8y_2E0 all V9z_2E0 (s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINL_2E1(s(A_27e,V9z_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINL_2E1(s(A_27e,V7x_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINR_2E1(s(A_27f,V8y_2E0))))) <-> s(A_27e,V7x_2E0) = s(A_27e,V9z_2E0) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))) & (all V4x_2E0 all V5y_2E0 all V6z_2E0 (s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINL_2E1(s(A_27d,V6z_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINR_2E1(s(A_27c,V4x_2E0))),s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINL_2E1(s(A_27d,V5y_2E0))))) <-> -p(s(tyop_2Emin_2Ebool,V0P_2E0)) & s(A_27d,V5y_2E0) = s(A_27d,V6z_2E0))) & (all V1x_2E0 all V2y_2E0 all V3z_2E0 (s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,V1x_2E0))),s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINL_2E1(s(A_27b,V2y_2E0))))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,V3z_2E0))) <-> s(A_27a,V3z_2E0) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Esum_2Econd__sum__expand) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1227 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1228 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINR_2E0),s(A_27d,X0_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1229 (all A_27e all A_27f all X0_2E0 s(tyop_2Esum_2Esum(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Esum_2Esum(A_27e,A_27f)),c_2Esum_2EINR_2E0),s(A_27f,X0_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINR_2E1(s(A_27f,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1230 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Esum_2ENOT__ISR__ISL) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1231 (all A_27a all A_27b all V0P_2E0 ((all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))))) & (all V3y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3y_2E0))))))) <-> (all V1s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_2E0))))))) # label(thm_2Esum_2EFORALL__SUM) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1232 (all A_27c all X0_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),A_27c),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))) = s(A_27c,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1233 (all A_27a all V0x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) # label(thm_2Eoption_2ENOT__IS__SOME__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1234 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Eoption_2ENOT__SOME__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1235 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Eoption_2Eoption(A_27c),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MAP2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1236 (all A_27a all A_27b all V0e_2E0 all V1f_2E0 exists V2fn_2E0 ((all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27b),V2fn_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0)))) & s(A_27b,V0e_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27b),V2fn_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) # label(thm_2Eoption_2Eoption__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1237 (all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1238 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__CHOICE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__CHOICE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1239 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Eoption_2EOPTION__GUARD_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__GUARD_2E1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1240 (all A_27a all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1241 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1242 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f623_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1243 (all A_27a all V0P_2E0 ((all V1opt_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))))) # label(thm_2Eoption_2EFORALL__OPTION) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1244 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1245 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2m_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0),s(A_27c,V2m_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MCOMP_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0),s(A_27c,V2m_2E0)))) # label(thm_2Eoption_2EOPTION__MCOMP__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1246 (all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) = s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1247 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1248 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1249 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1250 (all A_27a s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) # label(thm_2Eoption_2ENONE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1251 (all A_27a ((all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V1P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Eoption_2EOPTION__ALL__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1252 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1253 (all A_27a all A_27b all A_27c all V0v_2E0 all V1o2_2E0 all V2o1_2E0 all V3f_2E0 (s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2o1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0))) <-> (exists V4x1_2E0 exists V5x2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V2o1_2E0) & s(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V5x2_2E0))) & s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3f_2E0),s(A_27a,V4x1_2E0))),s(A_27b,V5x2_2E0))) = s(A_27c,V0v_2E0))))) # label(thm_2Eoption_2EOPTION__MAP2__SOME) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1254 (all A_27a all A_27b ((all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V1f_2E0 all V2x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V2x_2E0)))))) # label(thm_2Eoption_2EOPTION__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1255 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1256 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1257 (all A_27a all A_27b all V0v_2E0 all V1sc_2E0 all V2opt_2E0 all V3nc_2E0 (s(A_27b,V0v_2E0) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0),s(A_27b,V3nc_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0))) <-> s(A_27b,V0v_2E0) = s(A_27b,V3nc_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) | (exists V4x_2E0 (s(A_27b,V0v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0),s(A_27a,V4x_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))))))) # label(thm_2Eoption_2Eoption__case__eq) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1258 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) # label(thm_2Eoption_2EOPTION__MAP__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1259 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f674_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f674_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef674_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1260 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)) # label(thm_2Eoption_2Eoption__case__ID) # label(axiom) # label(non_clause). [assumption]. 19.81/19.98 1261 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))))) & ((all V3x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Eoption_2Esome__intro) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1262 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f605_0_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),f605_0_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0)))) # label(arityeq1_2Ef605_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1263 (all A_27a all V0Q_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))) -> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))))) | (all V3x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))) # label(thm_2Eoption_2Esome__elim) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1264 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1265 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Esum_2EINR_2E0),s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1266 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1267 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1268 (all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1269 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Eoption_2Eoption__REP_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Eoption__REP_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1270 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f674_1_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_1_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef674_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1271 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1272 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1273 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1274 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1275 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 all V2e_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))),s(A_27b,V2e_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0)))) # label(thm_2Eoption_2Eoption__case__compute) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1276 (all A_27a all A_27b all V0x_2E0 all V2f_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0x_2E0))) = s(A_27b,f667_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) # label(def0_2Ethm_2Eoption_2ESOME__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1277 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1278 (all A_27a all V0opt_2E0 ((exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))))) # label(thm_2Eoption_2EIS__SOME__EXISTS) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1279 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2e_2E0 ((all V3x_2E0 all V4y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) <-> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0))) & (all V5x_2E0 s(A_27a,V5x_2E0) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5x_2E0)))))) & (all V7x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V8x_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V8x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (all V13x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0)) & (all V17v_2E0 all V18f_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V17v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V18f_2E0))) = s(A_27b,V17v_2E0)) & (all V19x_2E0 all V20v_2E0 all V21f_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V19x_2E0))),s(A_27b,V20v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0),s(A_27a,V19x_2E0)))) & (all V24f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V24f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V25x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0)))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & (all V22f_2E0 all V23x_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V23x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(A_27a,V23x_2E0)))))) & (all V16x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0))) & (all V15x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0))))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) & (all V14x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0)))) -> s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(A_27b,V2e_2E0))) & (all V12x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0)) & (all V11x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0))))))) & (all V10x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> -p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0)))))) & (all V9x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0))) & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & (all V6x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1280 (all A_27a ((all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Eoption_2EIS__SOME__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1281 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1282 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Eoption_2ENOT__NONE__SOME) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1283 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1284 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1285 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1286 (all A_27a all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,f674_0_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0))) # label(def1_2Ethm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1287 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1288 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1289 (all A_27a all V0P_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) <-> (exists V1opt_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_2E0))))))) # label(thm_2Eoption_2EEXISTS__OPTION) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1290 (all A_27a all V0opt_2E0 all V1opt_27_2E0 all V2P_2E0 all V3P_27_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))))) # label(thm_2Eoption_2EOPTION__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1291 (all A_27a all V0opt_2E0 all V1P_27_2E0 all V2P_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_27_2E0),s(A_27a,V3x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))))))) # label(thm_2Eoption_2EOPTION__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1292 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1293 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),f667_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(A_27b,f667_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef667_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1294 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2Q_2E0 all V3P_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))))))) # label(thm_2Eoption_2EOPTREL__MONO) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1295 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1296 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))))) # label(thm_2Eoption_2ESOME__11) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1297 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1298 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f605_0_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1x_2E0)))) # label(def0_2Ethm_2Eoption_2Eoption__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1299 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1300 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1301 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1302 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1303 (all A_27a all V0m1_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__CHOICE__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1304 (all A_27a all A_27b all V0v_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4v_2E0 all V5f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V2M_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) & (s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) -> s(A_27b,V0v_27_2E0) = s(A_27b,V4v_2E0)) & (all V6x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(A_27a,V6x_2E0))))) -> s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V2M_2E0),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0))))) # label(thm_2Eoption_2Eoption__case__cong) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1305 (all A_27a ((all V1r_2E0 (s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1r_2E0))))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1r_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & (all V0a_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V0a_2E0)))) # label(thm_2Eoption_2Eoption__REP__ABS__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1306 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V1a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1a_2E0))))))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))))) # label(thm_2Eoption_2Eoption__Induct) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1307 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3x0_2E0 exists V4y0_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) & s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V4y0_2E0))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x0_2E0))),s(A_27b,V4y0_2E0)))))) | s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) & s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0)))))) # label(thm_2Eoption_2EOPTREL__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1308 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool)),f614_0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0))) = s(tyop_2Emin_2Ebool,f614_0_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0)))) # label(arityeq2_2Ef614_0_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1309 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f674_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef674_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1310 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1311 (all A_27b all A_27c all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f614_0_2E2(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0)))))) # label(def0_2Ethm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1312 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1313 (all A_27a all A_27b ((all V0f_2E0 all V1x_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))))) & (all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1314 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1315 (all A_27a all A_27b ((all V0f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V1x_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2f_2E0),s(A_27b,V1x_2E0)))))) # label(thm_2Eoption_2EOPTION__BIND__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1316 (all A_27a all A_27b all A_27c all V0v_2E0 all V1m_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1317 (all A_27a all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1318 (all A_27a all A_27b all V0opt1_2E0 all V1opt2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0))))) # label(thm_2Eoption_2EOPTION__MAP__CONG) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1319 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1320 (all A_27a all A_27b ((all V2x_2E0 all V3v_2E0 all V4f_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(A_27b,V3v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V2x_2E0)))) & (all V0v_2E0 all V1f_2E0 s(A_27b,V0v_2E0) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0)))))) # label(thm_2Eoption_2Eoption__case__def) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1321 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/19.99 1322 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1323 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1324 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Eoption__ABS_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Eoption__ABS_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1325 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__NONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1326 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1327 (all V0b_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__GUARD__COND) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1328 (all A_27a all V0opt_2E0 ((exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0)))) | s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))) # label(thm_2Eoption_2Eoption__CASES) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1329 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1330 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MAP2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1331 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eoption_2ESOME__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1332 (all A_27a all A_27b all A_27c all V0x_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1g_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EOPTION__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1333 (all A_27a all A_27b all A_27c all V0x_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EOPTION__MAP__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1334 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f623_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f623_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef623_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1335 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1336 (all A_27a all V0y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_0_2E1(s(A_27a,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_1_2E1(s(A_27a,V0y_2E0))))))) # label(thm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1337 (all A_27a all A_27b all V0x_2E0 all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1g_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EIS__SOME__BIND) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1338 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1339 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1340 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 ((s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0)))) # label(thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1341 (all A_27a all V0y_2E0 all V1x_2E0 all V2P_2E0 ((s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) & -p(s(tyop_2Emin_2Ebool,V2P_2E0)) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0)))) & (s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) & p(s(tyop_2Emin_2Ebool,V2P_2E0)) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,V2P_2E0))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> -p(s(tyop_2Emin_2Ebool,V2P_2E0))))) # label(thm_2Eoption_2EIF__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1342 (all A_27a s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f673_0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) # label(thm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1343 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1344 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f623_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f623_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef623_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1345 (all A_27a all A_27b all V0y_2E0 all V1p_2E0 all V2f_2E0 ((s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0))) <-> (exists V3x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V3x_2E0))))) | s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0)) & (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) <-> (exists V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1346 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__JOIN_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1347 (all A_27a all V0y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f674_1_2E2(s(A_27a,V0y_2E0),s(A_27a,V2x_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,V2x_2E0))) # label(def0_2Ethm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1348 (all A_27a all A_27b all V0o1_2E0 all V1o2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) -> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f1_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3f2_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3f2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f1_2E0))))) # label(thm_2Eoption_2EOPTION__BIND__cong) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1349 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1350 (all A_27a all A_27b all V0m1_2E0 all V1m2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),V0m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),V0m1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1m2_2E0)))))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1351 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),f667_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),f667_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef667_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1352 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2y_2E0 (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V2y_2E0))) <-> (exists V3z_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3z_2E0))) = s(A_27b,V2y_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3z_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))))) # label(thm_2Eoption_2EOPTION__MAP__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1353 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,f623_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))))) # label(def0_2Ethm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1354 (all A_27a all V0opt_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) | (exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0)))))) # label(thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1355 (all A_27a all V0x_2E0 all V1X_2E0 all V2P_2E0 ((s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V2P_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) <-> p(s(tyop_2Emin_2Ebool,V2P_2E0)) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0))) <-> s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) & -p(s(tyop_2Emin_2Ebool,V2P_2E0))) & ((p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,V2P_2E0))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))))) # label(thm_2Eoption_2EIF__NONE__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1356 (all A_27a all V0P_2E0 ((all V1a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1a_2E0))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))))) # label(thm_2Eoption_2Eoption__induction) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1357 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1358 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1359 (all A_27a ((all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__JOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1360 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1361 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f614_0_2E2(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0))))),s(A_27c,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1362 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0)))) # label(thm_2Eoption_2Eoption__case__SOME__ID) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1363 (all A_27a all A_27b all V0y_2E0 all V1m2_2E0 all V2m1_2E0 ((s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0) | s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0)) & ((exists V3x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0))) <-> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0)))))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1364 (all A_27a all A_27b all A_27c all A_27d all V0h_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0h_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0h_2E0)))))) # label(thm_2Eoption_2EOPTION__MCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1365 (all A_27a all V0P_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f623_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f623_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1366 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1367 (all A_27a all A_27b all A_27c all V0x1_2E0 all V1x2_2E0 all V2y1_2E0 all V3y2_2E0 all V4f1_2E0 all V5f2_2E0 ((all V6x_2E0 all V7y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0) & s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7y_2E0))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f1_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f2_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))))) & s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0) & s(tyop_2Eoption_2Eoption(A_27a),V0x1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0) -> s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f2_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0),s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0))))) # label(thm_2Eoption_2EOPTION__MAP2__cong) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1368 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1369 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f673_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f673_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef673_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1370 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f674_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f674_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef674_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1371 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1372 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1373 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eoption_2ETHE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1374 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),f667_0_2E1(s(A_27a,V0x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eoption_2ESOME__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1375 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f673_0_2E1(s(A_27a,V0x_2E0)))) # label(def0_2Ethm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1376 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1377 (all A_27a ((all V0m2_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0)))) & (all V1x_2E0 all V2m2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V2m2_2E0)))))) # label(thm_2Eoption_2EOPTION__CHOICE__def) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1378 (all A_27a (s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))))) # label(thm_2Eoption_2EIS__NONE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1379 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0y_2E0))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__MAP2__THM) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1380 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1381 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))))) # label(thm_2Eoption_2EOPTREL__refl) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1382 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1383 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1384 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_2E0) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0))))) # label(thm_2Eoption_2EOPTION__MCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1385 (all A_27c all X0_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1386 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.81/20.00 1387 (all A_27a all V0m2_2E0 all V1m1_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0))))) # label(thm_2Eoption_2EOPTION__CHOICE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1388 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f623_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,f623_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef623_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1389 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1390 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))),s(A_27c,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MCOMP_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),X1_2E0),s(A_27c,X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MCOMP_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1391 (all A_27a all A_27b all A_27c all V0o2_2E0 all V1o1_2E0 all V2f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) | s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V0o2_2E0) <-> s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1o1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0o2_2E0))))) # label(thm_2Eoption_2EOPTION__MAP2__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1392 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTION__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__ALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1393 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),f605_0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),V0rep_2E0))))) # label(thm_2Eoption_2Eoption__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1394 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Eoption_2ESOME_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1395 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1396 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0x_2E0)))))) # label(thm_2Eoption_2ESOME__SOME__APPLY) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1397 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) # label(thm_2Eoption_2EIS__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1398 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1399 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1400 (all V0b_2E0 ((s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0b_2E0))) & (s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0b_2E0))))) # label(thm_2Eoption_2EOPTION__GUARD__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1401 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) # label(thm_2Eoption_2EOPTION__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1402 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1403 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_2E0))) <-> s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))))))) # label(thm_2Eoption_2EOPTION__JOIN__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1404 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1405 (all A_27a all V0x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EIS__NONE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1406 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1407 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1408 (all A_27a all X0_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1409 (all A_27a all A_27b all V0option_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),A_27b)),V0option_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))))))) # label(thm_2Eoption_2Edatatype__option) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1410 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0)))) # label(thm_2Eoption_2EOPTION__APPLY__MAP2) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1411 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1412 (all A_27a all A_27b all V0d_2E0 all V1c_2E0 all V2b_2E0 all V3a_2E0 all V4R2_2E0 all V5R1_2E0 (s(A_27a,V3a_2E0) = s(A_27a,V1c_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R2_2E0),s(A_27b,V2b_2E0))),s(A_27b,V0d_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R1_2E0),s(A_27a,V3a_2E0))),s(A_27a,V1c_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V2b_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1c_2E0),s(A_27b,V0d_2E0)))))))) # label(thm_2Epair_2ELEX__DEF__THM) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1413 (all A_27a all A_27b all V0P_2E0 ((exists V1x_2E0 exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f718_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))))) # label(thm_2Epair_2EPEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1414 (all A_27a all A_27b all A_27c all A_27d all V0P_2E0 all V2N_2E0 all V5x_2E0 all V6y_2E0 s(A_27d,f724_1_2E4(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V5x_2E0))),s(A_27b,V6y_2E0)))))) # label(def0_2Ethm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1415 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Epair_2ECURRY_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epair_2ECURRY_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1416 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f693_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f693_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef693_1_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1417 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1418 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f717_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f717_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef717_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1419 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f693_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f693_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef693_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1420 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1421 (all A_27a all A_27b all A_27c all V2N_2E0 all V3x_2E0 all V4y_2E0 s(A_27c,f724_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))) # label(def1_2Ethm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1422 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f708_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f708_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0)))) # label(arityeq1_2Ef708_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1423 (all A_27a all A_27b all A_27c all A_27d all V0p_2E0 all V1f_2E0 all V2g_2E0 s(A_27d,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0)))))) # label(thm_2Epair_2ESND__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1424 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0))),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1425 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1426 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),f730_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),f730_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef730_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1427 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2p_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))))))) # label(thm_2Epair_2EPAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1428 (all A_27a all A_27b all A_27c all V0P_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,f730_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),f730_2_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0)))))) # label(def1_2Ethm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1429 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1430 (all A_27a all A_27b all V0P_2E0 ((all V2p__1_2E0 all V3p__2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2p__1_2E0),s(A_27b,V3p__2_2E0))))))) <-> (all V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))) # label(thm_2Epair_2EFORALL__PROD) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1431 (all A_27a all A_27b all X0_2E0 s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1432 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f717_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,f717_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef717_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1433 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1434 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1435 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1436 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 all X5_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f693_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0))),s(A_27a,X4_2E0))),s(A_27b,X5_2E0))) = s(tyop_2Emin_2Ebool,f693_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0),s(A_27a,X4_2E0),s(A_27b,X5_2E0)))) # label(arityeq6_2Ef693_1_2E6_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1437 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))) # label(thm_2Epair_2EUNCURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.81/20.01 1438 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0g_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1f_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1f_2E0))))) # label(thm_2Epair_2ECURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1439 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1440 (all A_27a all A_27b all A_27c all A_27d all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),V1f_2E0))),s(A_27d,V0x_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),V1f_2E0))),s(A_27d,V0x_2E0)))) # label(thm_2Epair_2EC__UNCURRY__L) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1441 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27d_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1442 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f718_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f718_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef718_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1443 (all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1444 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1445 (all A_27b all A_27c all X0_2E0 s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1446 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(A_27d,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1447 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1448 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2b_2E0 all V3a_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V2b_2E0))) <-> s(A_27b,V2b_2E0) = s(A_27b,V0y_2E0) & s(A_27a,V1x_2E0) = s(A_27a,V3a_2E0))) # label(thm_2Epair_2EPAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1449 (all A_27a all A_27b exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f682_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0rep_2E0))))) # label(thm_2Epair_2Eprod__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1450 (all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1451 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1452 (all A_27a all A_27b all V0a_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ESWAP_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0))),s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0)))))) # label(thm_2Epair_2ESWAP__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1453 (all A_27a1 all A_27a2 all A_27b all A_27c all V1N_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),f725_0_2E3(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27a1,V3x_2E0),s(A_27a2,V4y_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27a1,V3x_2E0))),s(A_27a2,V4y_2E0)))) # label(def1_2Ethm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1454 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1455 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f719_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f719_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef719_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1456 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1457 (all A_27a all A_27b all V0P_2E0 ((exists V2p__1_2E0 exists V3p__2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2p__1_2E0),s(A_27b,V3p__2_2E0))))))) <-> (exists V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))) # label(thm_2Epair_2EEXISTS__PROD) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1458 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0)))))) # label(thm_2Epair_2EFORALL__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 19.88/20.01 1459 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1460 (all A_27a all A_27b all V0P_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0))) = s(tyop_2Emin_2Ebool,f718_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0)))) # label(def0_2Ethm_2Epair_2EPEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1461 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1462 (all A_27a all A_27b all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f720_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epair_2EELIM__PFORALL__EVAL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1463 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ERPROD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epair_2ERPROD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2ERPROD_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1464 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1465 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1466 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1467 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Epair_2Esymmetric__LEX) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1468 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1469 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1470 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (p(s(tyop_2Emin_2Ebool,f684_0_2E4(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0),s(A_27a,V2a_2E0),s(A_27b,V3b_2E0)))) <-> s(A_27a,V2a_2E0) = s(A_27a,V0x_2E0) & s(A_27b,V3b_2E0) = s(A_27b,V1y_2E0))) # label(def0_2Ethm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1471 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1472 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0))) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V1x_2E0),s(A_27c,V0y_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0)))) # label(thm_2Epair_2Epair__case__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1473 (all A_27a all A_27b all V0R1_2E0 all V2s_2E0 all V1R2_2E0 all V3t_2E0 all V4u_2E0 all V5v_2E0 (p(s(tyop_2Emin_2Ebool,f693_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0),s(A_27a,V4u_2E0),s(A_27b,V5v_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0))),s(A_27b,V5v_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0))),s(A_27a,V4u_2E0)))))) # label(def0_2Ethm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1474 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2s_2E0 all V3t_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f693_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f693_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2s_2E0),s(A_27b,V3t_2E0)))) # label(def1_2Ethm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1475 (all A_27a all A_27b all X0_2E0 s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1476 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2Q_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0)))))))) # label(thm_2Epair_2EPROD__ALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1477 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1478 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))) <-> s(A_27b,V3b_2E0) = s(A_27b,V1y_2E0) & s(A_27a,V0x_2E0) = s(A_27a,V2a_2E0))) # label(thm_2Epair_2ECLOSED__PAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1479 (all A_27a all A_27b all V0x_2E0 exists V1q_2E0 exists V2r_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1q_2E0),s(A_27b,V2r_2E0)))) # label(thm_2Epair_2EABS__PAIR__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1480 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f693_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f693_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef693_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1481 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EPROD__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epair_2EPROD__ALL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1482 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1483 (all A_27a all A_27b all V0P_2E0 ((exists V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))) <-> (exists V2p1_2E0 exists V3p2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2p1_2E0))),s(A_27b,V3p2_2E0))))))) # label(thm_2Epair_2EELIM__PEXISTS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1484 (all A_27a all A_27b all A_27c all V0p_2E0 all V1f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0),s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),V0p_2E0))))),s(A_27c,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),V0p_2E0))))) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V0p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0)))) # label(thm_2Epair_2Epair__CASE__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1485 (all A_27a all A_27b all A_27c all V0f_27_2E0 all V1M_2E0 all V2M_27_2E0 all V3f_2E0 (s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),V1M_2E0) & (all V4x_2E0 all V5y_2E0 (s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(A_27c,V5y_2E0))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_27_2E0),s(A_27b,V4x_2E0))),s(A_27c,V5y_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V3f_2E0),s(A_27b,V4x_2E0))),s(A_27c,V5y_2E0))))) -> s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_27_2E0))) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V1M_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V3f_2E0))))) # label(thm_2Epair_2Epair__case__cong) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1486 (all A_27b all A_27c all X0_2E0 s(A_27c,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1487 (all A_27a all A_27b all V0p_2E0 all V1Q_27_2E0 all V2Q_2E0 all V3P_27_2E0 all V4P_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(A_27b,V6y_2E0)))))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V5x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))))) # label(thm_2Epair_2EPROD__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1488 (all A_27a all A_27b all V0P_2E0 ((all V2p1_2E0 all V3p2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2p1_2E0))),s(A_27b,V3p2_2E0))))) <-> (all V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))))) # label(thm_2Epair_2EELIM__PFORALL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1489 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f718_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f718_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef718_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1490 (all A_27a all A_27b all V0P_2E0 ((all V1p__1_2E0 all V2p__2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1p__1_2E0),s(A_27b,V2p__2_2E0))))))) -> (all V3p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3p_2E0))))))) # label(thm_2Epair_2Epair__induction) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1491 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1492 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epair_2ELEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2ELEX_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1493 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27d_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27d_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1494 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V1x_2E0),s(A_27c,V0y_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0)))) # label(thm_2Epair_2Epair__case__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1495 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1496 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Epair_2Etransitive__LEX) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1497 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0)) # label(thm_2Epair_2EUNCURRY__CURRY__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1498 (all A_27a all A_27b all A_27c all V0f_2E0 exists V1fn_2E0 all V2x_2E0 all V3y_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1fn_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) # label(thm_2Epair_2Epair__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1499 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1500 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1501 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epair_2ELEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Epair_2ELEX_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1502 (all A_27a all A_27b all V0P_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2x_2E0))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f719_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))))) # label(thm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1503 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1504 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0)) # label(thm_2Epair_2ECURRY__UNCURRY__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1505 (all A_27a1 all A_27a2 all A_27b all A_27c all V0M_2E0 all V1N_2E0 all V2b_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),f725_1_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27b,V2b_2E0))))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),V0M_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),f725_0_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0))))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),V0M_2E0))),s(A_27b,V2b_2E0)))) # label(thm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1506 (all A_27a1 all A_27a2 all A_27b all A_27c all V1N_2E0 all V2b_2E0 all V5x_2E0 all V6y_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27a1,V5x_2E0))),s(A_27a2,V6y_2E0))),s(A_27b,V2b_2E0))) = s(A_27c,f725_1_2E4(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27b,V2b_2E0),s(A_27a1,V5x_2E0),s(A_27a2,V6y_2E0)))) # label(def0_2Ethm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1507 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f684_0_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))) # label(thm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1508 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1509 (all A_27a all A_27b all A_27c all V0P_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V1f_2E0))) = s(tyop_2Emin_2Ebool,f730_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V1f_2E0)))) # label(def2_2Ethm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1510 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1511 (all A_27a all A_27b all V0p_2E0 all V1q_2E0 (s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) & s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))) <-> s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) # label(thm_2Epair_2EPAIR__FST__SND__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1512 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f684_0_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f684_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef684_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1513 (all A_27a all A_27b all A_27c all V0v_2E0 all V1p_2E0 all V2f_2E0 ((exists V3x_2E0 exists V4y_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V3x_2E0))),s(A_27c,V4y_2E0))) = s(A_27a,V0v_2E0) & s(tyop_2Epair_2Eprod(A_27b,A_27c),V1p_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V3x_2E0),s(A_27c,V4y_2E0))))) <-> s(A_27a,V0v_2E0) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0))))) # label(thm_2Epair_2Epair__case__eq) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1514 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))))))) # label(thm_2Epair_2EPROD__ALL__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1515 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1516 (all A_27a all A_27b ((all V1r_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1r_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2EREP__prod_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1r_2E0))))) <-> (exists V2x_2E0 exists V3y_2E0 all V4x_27_2E0 all V5x_27_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1r_2E0),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))) <-> s(A_27b,V5x_27_27_2E0) = s(A_27b,V3y_2E0) & s(A_27a,V4x_27_2E0) = s(A_27a,V2x_2E0))))) & (all V0a_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),V0a_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2EREP__prod_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0a_2E0)))))))) # label(thm_2Epair_2EABS__REP__prod) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1517 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f719_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f719_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef719_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.02 1518 (all A_27a all A_27b all V0R1_2E0 all V2s_2E0 all V1R2_2E0 all V3t_2E0 all V4u_2E0 all V5v_2E0 (p(s(tyop_2Emin_2Ebool,f692_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0),s(A_27a,V4u_2E0),s(A_27b,V5v_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0))),s(A_27b,V5v_2E0)))) & s(A_27a,V4u_2E0) = s(A_27a,V2s_2E0) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0))),s(A_27a,V4u_2E0)))))) # label(def0_2Ethm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1519 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),f725_0_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)))),f725_0_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0)))) # label(arityeq1_2Ef725_0_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1520 (all A_27a1 all A_27a2 all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a1_2CA_27a2_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1521 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f724_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f724_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ef724_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1522 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f692_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f692_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef692_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1523 (all A_27a all A_27b all V0P_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Emin_2Ebool,f717_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))) # label(def0_2Ethm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1524 (all A_27a all A_27b all V0R_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ERPROD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))))))) # label(thm_2Epair_2EWF__RPROD) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1525 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1526 (all A_27a all A_27b all V0y_2E0 all V1p_2E0 ((exists V2x_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27a),V1p_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V0y_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V1p_2E0))))) # label(thm_2Epair_2ESND__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1527 (all A_27a all A_27b all X0_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2EABS__prod_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EABS__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1528 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f692_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))) # label(thm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1529 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1530 (all A_27a all A_27b all A_27c all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),f730_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),f730_1_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1531 (all A_27a all A_27b all A_27c all V0f_27_2E0 all V1f_2E0 all V2M_27_2E0 all V3M_2E0 ((all V4x_2E0 all V5y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V2M_27_2E0) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_27_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))))) & s(tyop_2Epair_2Eprod(A_27a,A_27b),V3M_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V2M_27_2E0) -> s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2M_27_2E0))) = s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3M_2E0))))) # label(thm_2Epair_2EUNCURRY__CONG) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1532 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool)),f730_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),f730_1_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef730_1_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1533 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27d,f724_1_2E4(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)))),f724_1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef724_1_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1534 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))))) # label(thm_2Epair_2Ereflexive__LEX) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1535 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 all X5_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f692_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0))),s(A_27a,X4_2E0))),s(A_27b,X5_2E0))) = s(tyop_2Emin_2Ebool,f692_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0),s(A_27a,X4_2E0),s(A_27b,X5_2E0)))) # label(arityeq6_2Ef692_1_2E6_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1536 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1537 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1538 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2EREP__prod_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2EREP__prod_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EREP__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1539 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1540 (all A_27a all A_27b all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f719_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1541 (all A_27a all A_27b all A_27c all V0pair_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),A_27c),V0pair_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0))))))) # label(thm_2Epair_2Edatatype__pair) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1542 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1543 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1544 (all A_27a all A_27b all V0p_2E0 all V1p_27_2E0 all V2P_2E0 all V3P_27_2E0 all V4Q_2E0 all V5Q_27_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0) & (all V6x_2E0 all V7y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V6x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V6x_2E0))))) & (all V8x_2E0 all V9y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8x_2E0),s(A_27b,V9y_2E0))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V9y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(A_27b,V9y_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) # label(thm_2Epair_2EPROD__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1545 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(A_27c,c_2Epair_2ECURRY_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0),s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0)))))) # label(thm_2Epair_2ECURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1546 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27c,f725_1_2E4(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27b,X1_2E0),s(A_27a1,X2_2E0),s(A_27a2,X3_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a2,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)))),f725_1_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a1,X2_2E0))),s(A_27a2,X3_2E0)))) # label(arityeq4_2Ef725_1_2E4_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1547 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1548 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1549 (all A_27a all A_27b all X0_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ESWAP_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2ESWAP_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESWAP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1550 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1551 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1552 (all A_27c all A_27d all X0_2E0 s(A_27d,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),A_27d),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1553 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a1_2CA_27a2_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1554 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2s_2E0 all V3t_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f692_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2s_2E0),s(A_27b,V3t_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f692_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0)))))) # label(def1_2Ethm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1555 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1556 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,f724_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f724_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef724_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1557 (all A_27a all A_27b all A_27c all A_27d all V0p_2E0 all V1f_2E0 all V2g_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) = s(A_27c,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0)))))) # label(thm_2Epair_2EFST__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1558 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1559 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Emin_2Efun_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27d_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1560 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1561 (all A_27a all A_27b all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f720_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))) <-> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2x_2E0))))))))) # label(thm_2Epair_2EELIM__PFORALL__EVAL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1562 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1563 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1564 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0)))))) # label(thm_2Epair_2ES__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1565 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27d,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1566 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1567 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1568 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),f730_2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),f730_2_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef730_2_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1569 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1570 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f684_0_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f684_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef684_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1571 (all A_27a all A_27b all A_27c all V0f_2E0 all V1v_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0)))))) # label(thm_2Epair_2EUNCURRY__VAR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1572 (all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1573 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f720_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f720_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef720_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1574 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),f724_1_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)))),f724_1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ef724_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1575 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0)))))) # label(thm_2Epair_2Eo__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1576 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1577 (all A_27a all A_27b all V0x_2E0 exists V1q_2E0 exists V2r_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1q_2E0),s(A_27b,V2r_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0)) # label(thm_2Epair_2Epair__CASES) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1578 (all A_27a1 all A_27a2 all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1579 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1580 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 19.88/20.03 1581 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1582 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,f708_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f708_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef708_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1583 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1584 (all A_27a all A_27b all A_27c all V0P_2E0 all V1x_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f708_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0)))) # label(thm_2Epair_2ELAMBDA__PROD) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1585 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,f682_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f682_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef682_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1586 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27b,V1y_2E0) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))))) # label(thm_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1587 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0)))))) # label(thm_2Epair_2EELIM__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1588 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1589 (all A_27a all A_27b all A_27c all A_27d all V0P_2E0 all V1M_2E0 all V2N_2E0 s(A_27d,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),f724_1_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0))))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1M_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f724_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0))))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1M_2E0)))))) # label(thm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1590 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1591 (all A_27a all A_27b all V0x_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0)) # label(thm_2Epair_2EPAIR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1592 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1593 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),f730_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Ebool,f730_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ef730_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1594 (all A_27a all A_27b all A_27c all V2p_2E0 all V3a_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0))),s(A_27a,V3a_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0))),s(A_27a,V3a_2E0))))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),f730_2_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0),s(A_27a,V3a_2E0)))) # label(def0_2Ethm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1595 (all A_27a all A_27b all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1596 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2R4_2E0 all V3R3_2E0 all V4R2_2E0 all V5R1_2E0 ((all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R1_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R2_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))) & (all V8x_2E0 all V9y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R3_2E0),s(A_27b,V8x_2E0))),s(A_27b,V9y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R4_2E0),s(A_27b,V8x_2E0))),s(A_27b,V9y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R3_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R4_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0y_2E0))))))) # label(thm_2Epair_2ELEX__MONO) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1597 (all A_27a all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1598 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Epair_2Etotal__LEX) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1599 (all A_27a all A_27b all V1p_2E0 (p(s(tyop_2Emin_2Ebool,f682_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1p_2E0)))) <-> (exists V2x_2E0 exists V3y_2E0 all V4x_27_2E0 all V5x_27_27_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V4x_27_2E0) & s(A_27b,V5x_27_27_2E0) = s(A_27b,V3y_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1p_2E0),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))))))) # label(def0_2Ethm_2Epair_2Eprod__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1600 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1601 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),f730_2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),f730_2_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0)))) # label(arityeq1_2Ef730_2_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1602 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f730_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool)),f730_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X1_2E0)))) # label(arityeq2_2Ef730_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1603 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1604 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V1g_2E0),s(A_27c,V3y_2E0))))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V1g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27c,V3y_2E0)))))) # label(thm_2Epair_2EPAIR__MAP__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1605 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1606 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2v1_2E0 all V3v2_2E0 all V4R1_27_2E0 all V5R2_27_2E0 all V6v1_27_2E0 all V7v2_27_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v1_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0) & s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v2_2E0) & (all V12a_2E0 all V13b_2E0 all V14c_2E0 all V15d_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V14c_2E0),s(A_27b,V15d_2E0))) & s(A_27a,V12a_2E0) = s(A_27a,V14c_2E0) & s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V12a_2E0),s(A_27b,V13b_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5R2_27_2E0),s(A_27b,V13b_2E0))),s(A_27b,V15d_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V13b_2E0))),s(A_27b,V15d_2E0))))) & (all V8a_2E0 all V9b_2E0 all V10c_2E0 all V11d_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8a_2E0),s(A_27b,V9b_2E0))) & s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10c_2E0),s(A_27b,V11d_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R1_27_2E0),s(A_27a,V8a_2E0))),s(A_27a,V10c_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8a_2E0))),s(A_27a,V10c_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R1_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5R2_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0))))) # label(thm_2Epair_2ELEX__CONG) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1607 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1608 (all A_27a all A_27b all A_27c all V0P_2E0 all V2p1_2E0 all V3p2_2E0 s(A_27c,f708_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0),s(A_27a,V2p1_2E0),s(A_27b,V3p2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2p1_2E0),s(A_27b,V3p2_2E0)))))) # label(def0_2Ethm_2Epair_2ELAMBDA__PROD) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1609 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1610 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0))) # label(thm_2Epair_2EUNCURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1611 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f692_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f692_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef692_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1612 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1613 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ERPROD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f693_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))) # label(thm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1614 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1615 (all A_27a all A_27b all V0x_2E0 all V1p_2E0 ((exists V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V2y_2E0)))) <-> s(A_27a,V0x_2E0) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))) # label(thm_2Epair_2EFST__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1616 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1617 (all A_27a all A_27b all A_27c all V0f_2E0 all V1v_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))))) = s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0)))) # label(thm_2Epair_2EUNCURRY) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1618 (all A_27a all A_27b all V0R_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))))))) # label(thm_2Epair_2EWF__LEX) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1619 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),f725_1_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)))),f725_1_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef725_1_2E2_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1620 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)))),f725_0_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27a1,X1_2E0))),s(A_27a2,X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),f725_0_2E3(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27a1,X1_2E0),s(A_27a2,X2_2E0)))) # label(arityeq3_2Ef725_0_2E3_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1621 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f720_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f720_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef720_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1622 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1623 (all A_27a all A_27b all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f717_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))) <-> (all V1x_2E0 all V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))))) # label(thm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1624 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f692_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f692_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef692_1_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1625 (all A_27c all A_27d all X0_2E0 s(A_27c,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),A_27c),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1626 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1627 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1628 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__0) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1629 (all A_27a all V0f_2E0 all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,f765_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) <-> s(A_27a,V4y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3x_2E0))))) # label(def1_2Ethm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1630 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1631 (all A_27a all V0f_2E0 all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,f765_1_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) <-> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5x_2E0))) = s(A_27a,V6y_2E0))) # label(def0_2Ethm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1632 (all V4x_2E0 all V5y_2E0 (s(tyop_2Enum_2Enum,V5y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4x_2E0))) <-> p(s(tyop_2Emin_2Ebool,f764_1_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V5y_2E0)))))) # label(def0_2Ethm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1633 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1634 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2ESIMP__REC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2ESIMP__REC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2ESIMP__REC_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1635 (all A_27a all V0P_2E0 all V1R_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2a_2E0)))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> (exists V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))))) -> (exists V5f_2E0 (s(A_27a,V2a_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V6n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0)))))))))))))) # label(thm_2Eprim__rec_2EDC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1636 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0)))) # label(thm_2Eprim__rec_2Emeasure__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1637 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2EEQ__LESS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1638 (all A_27a all V0f_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2y_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Emeasure_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) # label(thm_2Eprim__rec_2Emeasure__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1639 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1640 (all A_27a all V0x_2E0 all V1f_27_2E0 all V2n_2E0 exists V3g_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1641 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1642 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1643 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Eprim__rec_2ELESS__REFL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1644 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f747_0_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f747_1_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1645 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1646 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f766_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V1y_2E0))) # label(def0_2Ethm_2Eprim__rec_2ELESS__ALT) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1647 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2EPRIM__REC__FUN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Eprim__rec_2EPRIM__REC__FUN_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1648 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1649 (all A_27a all V0x_2E0 all V1f_2E0 all V2n_2E0 exists V3fun_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Eprim__rec_2ESIMP__REC__EXISTS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1650 (all A_27a all V0e_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),f785_0_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))))))) # label(thm_2Eprim__rec_2Enum__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1651 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1652 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))),f785_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),f785_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) # label(arityeq2_2Ef785_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1653 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f779_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,f779_0_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef779_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1654 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__SUC__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1655 (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,f764_0_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))) <-> s(tyop_2Enum_2Enum,V3y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) # label(def1_2Ethm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1656 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_0_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_1_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1657 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1658 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1659 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1660 (all A_27a all V0x_2E0 all V1f_2E0 all V2g1_2E0 all V3g2_2E0 all V4m1_2E0 all V5m2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g1_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4m1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))) -> (all V6n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V4m1_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g1_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))))) # label(thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1661 (all A_27a all V0x_2E0 all V1f_2E0 ((all V2n_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,V0x_2E0)) & (all V3m_2E0 all V4n_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3m_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(thm_2Eprim__rec_2EPRIM__REC__EQN) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1662 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1663 (all A_27a all V0x_2E0 all V1f_2E0 all V2n_2E0 all V3y_2E0 ((exists V4g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) & s(A_27a,V3y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f779_0_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V3y_2E0)))))) # label(def0_2Ethm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1664 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eprim__rec_2EPRIM__REC_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eprim__rec_2EPRIM__REC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1665 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> (exists V2P_2E0 ((all V3n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1666 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__MONO) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1667 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Eprim__rec_2ELESS__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1668 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1669 (all A_27a all V0x_2E0 all V1f_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f779_0_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1670 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Emeasure_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eprim__rec_2Emeasure_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1671 (all A_27a all V0x_2E0 all V2n_2E0 s(A_27a,f750_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,V0x_2E0)) # label(def1_2Ethm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1672 (all A_27a all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2ESIMP__REC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f750_0_2E1(s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2EPRIM__REC__FUN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0)))) # label(thm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1673 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1674 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1675 (all X0_2E0 (-p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1676 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ESUC__LESS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.04 1677 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1678 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1679 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1680 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1681 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ef765_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1682 (all A_27a all V0x_2E0 all V1f_2E0 (s(A_27a,V0x_2E0) = s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V2m_2E0 s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))))) # label(thm_2Eprim__rec_2ESIMP__REC__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1683 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f764_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef764_1_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1684 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1685 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1686 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f764_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef764_0_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1687 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,f750_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f750_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef750_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1688 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f788_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f788_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef788_0_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1689 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))) = s(tyop_2Enum_2Enum,V0m_2E0)) # label(thm_2Eprim__rec_2EPRE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1690 (all V0m_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f747_0_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(def0_2Ethm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1691 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__LEMMA2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1692 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X0_2E0) = s(A_27a,X1_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1693 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1694 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f747_1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f747_1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef747_1_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1695 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f765_1_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef765_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1696 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f766_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f766_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef766_0_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1697 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) != s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Eprim__rec_2ESUC__ID) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1698 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1699 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1700 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(A_27a,f750_0_2E2(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef750_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1701 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f750_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0)))) # label(arityeq1_2Ef750_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1702 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0) <-> p(s(tyop_2Emin_2Ebool,f747_1_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(def1_2Ethm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1703 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1704 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1705 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Eprim__rec_2ESIMP__REC__REL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Eprim__rec_2ESIMP__REC__REL_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1706 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1707 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eprim__rec_2Ewellfounded_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Ewellfounded_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1708 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1709 (all A_27a all V0f_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_1_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,V1m_2E0),s(A_27a,V2n_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V1m_2E0))),s(A_27a,V2n_2E0)))) # label(thm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1710 (all X0_2E0 s(tyop_2Emin_2Ebool,f747_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f747_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef747_0_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1711 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> -(exists V1f_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Eprim__rec_2Ewellfounded__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1712 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv__image_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1713 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1714 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1715 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1716 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2EPRIM__REC__FUN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2EPRIM__REC__FUN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2EPRIM__REC__FUN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1717 (all A_27a all V0x_2E0 all V1f_2E0 all V2m_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))) # label(thm_2Eprim__rec_2EPRIM__REC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1718 (all A_27a all V0fun_2E0 all V1x_2E0 all V2f_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) <-> (all V4m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4m_2E0))))))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V1x_2E0))) # label(thm_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1719 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f747_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f747_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef747_1_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1720 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1721 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1722 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f788_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) # label(def0_2Ethm_2Eprim__rec_2EWF__PRED) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1723 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1724 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1725 (all A_27a all V1f_2E0 all V3fun_2E0 all V4n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,f750_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) # label(def0_2Ethm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1726 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Eprim__rec_2EINV__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1727 (all A_27a all V0e_2E0 all V1f_2E0 exists V2fn_2E0 ((all V3n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) & s(A_27a,V0e_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Eprim__rec_2Enum__Axiom) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1728 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eprim__rec_2ESIMP__REC_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eprim__rec_2ESIMP__REC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1729 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Eprim__rec_2ELESS__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1730 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_1_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ef765_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1731 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Eprim__rec_2ELESS__LEMMA1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1732 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Eprim__rec_2ENOT__LESS__0) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1733 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f765_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef765_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1734 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))),f785_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,f785_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0)))) # label(arityeq3_2Ef785_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1735 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1736 (all A_27a all V0m_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0))))))) # label(thm_2Eprim__rec_2EWF__measure) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1737 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) -> -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ENOT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1738 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f779_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f779_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef779_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1739 (all A_27a all V0e_2E0 all V1f_2E0 all V2fn1_2E0 (p(s(tyop_2Emin_2Ebool,f785_0_2E3(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0)))) <-> (all V3n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0e_2E0))) # label(def0_2Ethm_2Eprim__rec_2Enum__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1740 (all A_27a all V0x_2E0 all V1f_2E0 (s(A_27a,V0x_2E0) = s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V2m_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))),s(tyop_2Enum_2Enum,V2m_2E0))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0)))))))) # label(thm_2Eprim__rec_2EPRIM__REC__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1741 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1742 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f750_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef750_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1743 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Eprim__rec_2EWF__IFF__WELLFOUNDED) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1744 (all V3f_2E0 all V4a_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f815_3_2E2(s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),f815_2_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Enum_2Enum,V4a_2E0)))) # label(def5_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1745 (all V6n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V6n_2E0) <-> p(s(tyop_2Emin_2Ebool,f815_4_2E1(s(tyop_2Enum_2Enum,V6n_2E0)))))) # label(def2_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1746 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f816_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f816_1_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ef816_1_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1747 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2EODD__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1748 (all V0P_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1c_2E0)))) -> ((all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1c_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) & (all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))))) # label(thm_2Earithmetic_2EBOUNDED__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1749 (all V0m_2E0 all V1n_2E0 -(p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1750 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EFACT__LESS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1751 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V1n_2E0 all V2m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EEXP__BASE__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1752 (all V0f_2E0 ((all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) -> (all V2m_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))))) # label(thm_2Earithmetic_2ESTRICTLY__INCREASING__TC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1753 (all V0n_2E0 all V1p_2E0 all V2q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))))) # label(thm_2Earithmetic_2EMOD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1754 (all V0c_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0c_2E0),s(tyop_2Enum_2Enum,V0c_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2ESUB__EQUAL__0) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1755 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1756 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))),s(tyop_2Enum_2Enum,V0y_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))))) # label(thm_2Earithmetic_2EMOD__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1757 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1758 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Earithmetic_2ENUMERAL__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1759 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2EMAX__ASSOC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1760 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) # label(thm_2Earithmetic_2ELESS__ADD__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1761 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELE__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1762 (all V0n_2E0 -(p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN__AND__ODD) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1763 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMULT__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1764 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EODD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1765 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0))) # label(thm_2Earithmetic_2EMAX__EQ__0) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1766 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELEFT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1767 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EMULT__SYM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1768 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f1167_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(def0_2Ethm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1769 (all V0n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EODD__EVEN) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1770 (all V1a_2E0 all V0f_2E0 all V2m_2E0 all V3n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f816_3_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_4_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f816_2_2E4(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) # label(def2_2Ethm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1771 (all A_27a all V0x_2E0 all V1f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(A_27a,V0x_2E0)))) # label(thm_2Earithmetic_2EFUNPOW__1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1772 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EONE__MOD__IFF) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1773 (all V0n_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EADD__MODULUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1774 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1775 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2ELESS__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1776 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ERIGHT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1777 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1j_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__TIMES2) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1778 (all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V1y_2E0))) # label(thm_2Earithmetic_2EMULT__EQ__1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1779 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EMIN__COMM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1780 (all V1m_2E0 all V2a_2E0 all V3d_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V3d_2E0))),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V3d_2E0))))))))) = s(tyop_2Enum_2Enum,f1164_1_2E3(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3d_2E0)))) # label(def1_2Ethm_2Earithmetic_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1781 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Earithmetic_2ELESS__SUC__NOT) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1782 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1783 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELT__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1784 (all V0n_2E0 all V1m_2E0 ((s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1785 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__OR) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1786 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1787 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__0) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1788 (all A_27a all V0y_2E0 all V1x_2E0 all V2n_2E0 all V3R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) <-> (exists V4z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4z_2E0))),s(A_27a,V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V1x_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1789 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1790 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1082_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1082_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1082_0_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1791 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1792 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1793 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Earithmetic_2EABS__DIFF__EQ__0) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1794 (all A_27a all V0R_2E0 all V1m_2E0 all V2n_2E0 all V3x_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V3x_2E0),s(A_27a,V4z_2E0)))) -> (exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V1m_2E0),s(A_27a,V3x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V5y_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Earithmetic_2ENRC__ADD__E) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1795 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EADD__SUC) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1796 (all X0_2E0 s(tyop_2Emin_2Ebool,f1164_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1164_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1164_0_2E1) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1797 (all V0P_2E0 ((all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) <-> (all V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2ESUC__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 19.88/20.05 1798 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) & s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ear