0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n010.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1200 0.10/0.31 % DateTime : Tue Jul 13 15:18:36 EDT 2021 0.10/0.31 % CPUTime : 7.28/7.26 ============================== Prover9 =============================== 7.28/7.26 Prover9 (32) version 2009-11A, November 2009. 7.28/7.26 Process 31359 was started by sandbox2 on n010.cluster.edu, 7.28/7.26 Tue Jul 13 15:18:42 2021 7.28/7.26 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_30958_n010.cluster.edu". 7.28/7.26 ============================== end of head =========================== 7.28/7.26 7.28/7.26 ============================== INPUT ================================= 7.28/7.26 7.28/7.26 % Reading from file /tmp/Prover9_30958_n010.cluster.edu 7.28/7.26 7.28/7.26 set(prolog_style_variables). 7.28/7.26 set(auto2). 7.28/7.26 % set(auto2) -> set(auto). 7.28/7.26 % set(auto) -> set(auto_inference). 7.28/7.26 % set(auto) -> set(auto_setup). 7.28/7.26 % set(auto_setup) -> set(predicate_elim). 7.28/7.26 % set(auto_setup) -> assign(eq_defs, unfold). 7.28/7.26 % set(auto) -> set(auto_limits). 7.28/7.26 % set(auto_limits) -> assign(max_weight, "100.000"). 7.28/7.26 % set(auto_limits) -> assign(sos_limit, 20000). 7.28/7.26 % set(auto) -> set(auto_denials). 7.28/7.26 % set(auto) -> set(auto_process). 7.28/7.26 % set(auto2) -> assign(new_constants, 1). 7.28/7.26 % set(auto2) -> assign(fold_denial_max, 3). 7.28/7.26 % set(auto2) -> assign(max_weight, "200.000"). 7.28/7.26 % set(auto2) -> assign(max_hours, 1). 7.28/7.26 % assign(max_hours, 1) -> assign(max_seconds, 3600). 7.28/7.26 % set(auto2) -> assign(max_seconds, 0). 7.28/7.26 % set(auto2) -> assign(max_minutes, 5). 7.28/7.26 % assign(max_minutes, 5) -> assign(max_seconds, 300). 7.28/7.26 % set(auto2) -> set(sort_initial_sos). 7.28/7.26 % set(auto2) -> assign(sos_limit, -1). 7.28/7.26 % set(auto2) -> assign(lrs_ticks, 3000). 7.28/7.26 % set(auto2) -> assign(max_megs, 400). 7.28/7.26 % set(auto2) -> assign(stats, some). 7.28/7.26 % set(auto2) -> clear(echo_input). 7.28/7.26 % set(auto2) -> set(quiet). 7.28/7.26 % set(auto2) -> clear(print_initial_clauses). 7.28/7.26 % set(auto2) -> clear(print_given). 7.28/7.26 assign(lrs_ticks,-1). 7.28/7.26 assign(sos_limit,10000). 7.28/7.26 assign(order,kbo). 7.28/7.26 set(lex_order_vars). 7.28/7.26 clear(print_given). 7.28/7.26 7.28/7.26 % formulas(sos). % not echoed (5259 formulas) 7.28/7.26 7.28/7.26 ============================== end of input ========================== 7.28/7.26 7.28/7.26 % From the command line: assign(max_seconds, 1200). 7.28/7.26 7.28/7.26 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 7.28/7.26 7.28/7.26 % Formulas that are not ordinary clauses: 7.28/7.26 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_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]. 7.28/7.26 2 (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]. 7.28/7.26 3 (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]. 7.28/7.26 4 (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]. 7.28/7.26 5 (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]. 7.28/7.26 6 (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]. 7.28/7.26 7 (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]. 7.28/7.26 8 (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]. 7.28/7.26 9 (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]. 7.28/7.26 10 (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]. 7.28/7.26 11 (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]. 7.28/7.26 12 (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]. 7.28/7.26 13 (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]. 7.28/7.26 14 (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]. 7.28/7.26 15 (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]. 7.28/7.26 16 (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]. 7.28/7.26 17 (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]. 7.28/7.26 18 (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]. 7.28/7.26 19 (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]. 7.28/7.26 20 (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]. 7.28/7.26 21 (all A_27a all A_27b all 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)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))) # label(thm_2Ebool_2EONTO__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 22 (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]. 7.28/7.26 23 (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))) & (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,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,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))))) # label(thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 24 (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,V1t2_2E0)) & -p(s(tyop_2Emin_2Ebool,V0t1_2E0)) <-> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0))) # label(thm_2Ebool_2EEQ__EXPAND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 25 (all A_27a all V0i_2E0 s(tyop_2Ebool_2Eitself(A_27a),V0i_2E0) = s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)) # label(thm_2Ebool_2EITSELF__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 26 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0Q_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 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,V0Q_2E0)))) # label(thm_2Ebool_2ELEFT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 27 -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]. 7.28/7.26 28 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 29 (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]. 7.28/7.26 30 (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 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))))))) # label(thm_2Ebool_2EFORALL__itself) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 31 (all A_27a all F0_2E0 ((all V0x_2E0 all V1y_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_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)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0)))))) -> (all V0x_2E0 s(A_27a,c_2Emin_2E_40_2E1(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)),F0_2E0),s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)))) # label(thm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 32 (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]. 7.28/7.26 33 (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]. 7.28/7.26 34 (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]. 7.28/7.26 35 (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))) & ((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,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,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,V0t_2E0)) <-> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))))) # label(thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 36 (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]. 7.28/7.26 37 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0))) # label(thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 38 (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]. 7.28/7.26 39 (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,V1t2_2E0)))) # label(thm_2Ebool_2EAND2__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 40 (all A_27a all A_27b all V0x_2E0 all 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))) = s(A_27b,app_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]. 7.28/7.26 41 (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]. 7.28/7.26 42 (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)))))) <-> (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)))) # label(thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 43 (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]. 7.28/7.26 44 (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,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)))))) | (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]. 7.28/7.26 45 (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)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,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)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 46 (all A_27a all V0x_2E0 all 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),V1x_27_2E0)))) <-> (exists 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(thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 47 (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]. 7.28/7.26 48 (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]. 7.28/7.26 49 (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]. 7.28/7.26 50 (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]. 7.28/7.26 51 (all A_27a all F0_2E0 ((all V0a_2E0 all V1x_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V0a_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)),F0_2E0),s(A_27a,V0a_2E0))),s(A_27a,V1x_2E0)))))) -> (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(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)),F0_2E0),s(A_27a,V0a_2E0))))))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 52 (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]. 7.28/7.26 53 (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]. 7.28/7.26 54 (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]. 7.28/7.26 55 (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,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))))) # label(thm_2Ebool_2EDISJ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 56 (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]. 7.28/7.26 57 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)) & (-p(s(tyop_2Emin_2Ebool,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_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 58 (all A_27a all V0P_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))))) <-> -(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(thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 59 (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]. 7.28/7.26 60 (all A_27a all V0P_2E0 all V1Q_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 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))))))) & ((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)))))) & (p(s(tyop_2Emin_2Ebool,V1Q_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))))) <-> (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))))))))) # label(thm_2Ebool_2EPULL__FORALL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 61 (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)))) <-> ((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_2ELEFT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 62 (all A_27a all F0_2E0 all F2_2E0 all F1_2E0 ((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)))) <-> p(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))),F0_2E0),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)))))) -> ((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,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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(A_27a,V4x_2E0)))) -> ((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,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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V3x_2E0)))) -> (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),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))),F0_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))))))) # label(thm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 63 (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]. 7.28/7.26 64 (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_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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 65 (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__COMM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 66 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,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)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 67 (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]. 7.28/7.26 68 (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]. 7.28/7.26 69 (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)))) # label(thm_2Ebool_2ECONJ__COMM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 70 (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]. 7.28/7.26 71 (all A_27a all 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,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)))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 72 (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]. 7.28/7.26 73 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V3x_2E0 all V2a_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)),F1_2E0),s(A_27a,V3x_2E0))),s(A_27a,V2a_2E0)))) <-> s(A_27a,V2a_2E0) = s(A_27a,V3x_2E0))) -> ((all V2a_2E0 all V1t_2E0 all V0u_2E0 all V3x_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)),F1_2E0),s(A_27a,V3x_2E0))),s(A_27a,V2a_2E0))),s(A_27b,V1t_2E0),s(A_27b,V0u_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)))),F0_2E0),s(A_27a,V2a_2E0))),s(A_27b,V1t_2E0))),s(A_27b,V0u_2E0))),s(A_27a,V3x_2E0)))) -> (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),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)))),F0_2E0),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]. 7.28/7.26 74 (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]. 7.28/7.26 75 (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]. 7.28/7.26 76 (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]. 7.28/7.26 77 (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,V1Q_2E0) = s(tyop_2Emin_2Ebool,V0P_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_2Ebool__case__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 78 (all A_27a all A_27b all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),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))))) # label(thm_2Ebool_2EONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 79 (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]. 7.28/7.26 80 (all A_27a all V0P_2E0 all V1x_2E0 ((all 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,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))) = s(A_27a,V1x_2E0))) # label(thm_2Ebool_2ESELECT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 81 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_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),V1f_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4y_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0)))) -> ((all V0P_2E0 all V1f_2E0 all V3x_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))),F1_2E0),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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))),s(A_27a,V3x_2E0)))))) -> ((all V1f_2E0 all V2x_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)),F0_2E0),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)))) -> (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),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))),F1_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))))))))) # label(thm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 82 (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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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]. 7.28/7.26 83 (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]. 7.28/7.26 84 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 85 (all A_27a all V0P_2E0 all V1f_2E0 ((exists V2x_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_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_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]. 7.28/7.26 86 (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]. 7.28/7.26 87 (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,V0z_2E0)) & p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0)) & p(s(tyop_2Emin_2Ebool,V1y_2E0))))) # label(thm_2Ebool_2EMONO__AND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 88 (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]. 7.28/7.26 89 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 ((-p(s(tyop_2Emin_2Ebool,V0b_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,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))))) # label(thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 90 (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)) & 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,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,V2Q_2E0))))) # label(thm_2Ebool_2ELEFT__AND__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 91 (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]. 7.28/7.26 92 (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))))) & (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)))))) -> 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]. 7.28/7.26 93 (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)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 94 (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]. 7.28/7.26 95 (all A_27a all F0_2E0 ((all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 all V3x_2E0 ((s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) -> s(A_27a,V1x_27_2E0) = s(A_27a,V3x_2E0)) & (s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) -> s(A_27a,V3x_2E0) = s(A_27a,V2x_27_27_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)),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)))),F0_2E0),s(tyop_2Emin_2Ebool,V0x_2E0))),s(A_27a,V1x_27_2E0))),s(A_27a,V2x_27_27_2E0))),s(A_27a,V3x_2E0)))))) -> (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),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)))),F0_2E0),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]. 7.28/7.26 96 (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]. 7.28/7.26 97 (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__SYM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 98 (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]. 7.28/7.26 99 (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,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) # label(thm_2Ebool_2EOR__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 100 (all A_27a all A_27b all V0P_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))))) <-> (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_2Ebool_2ESWAP__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 101 (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]. 7.28/7.26 102 (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)))) <-> (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))))))) # label(thm_2Ebool_2EEXISTS__itself) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 103 (all A_27a all F0_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),F0_2E0),s(A_27a,V1x_2E0)))) -> (all V0P_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),F0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 104 (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,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2EBOTH__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 105 (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]. 7.28/7.26 106 (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]. 7.28/7.26 107 (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]. 7.28/7.26 108 (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,V1Q_2E0) = s(tyop_2Emin_2Ebool,V0P_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_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 109 (all A_27a all V0P_2E0 all 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)))))) <-> 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)))))) # label(thm_2Ebool_2ERES__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 110 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2M_2E0 all V3N_2E0 (s(A_27a,V2M_2E0) = s(A_27a,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),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),V1g_2E0),s(A_27a,V3N_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2M_2E0))))) # label(thm_2Ebool_2Eliteral__case__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 111 (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]. 7.28/7.26 112 (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]. 7.28/7.26 113 (all A_27a ((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)) & (all V0t1_2E0 all 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_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 114 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) & (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Ebool_2EBOTH__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 115 (all A_27a all F0_2E0 ((all V0P_2E0 all V1x_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)),F0_2E0),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)))) -> (all 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))))) <-> 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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))))))) # label(thm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.26 116 (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]. 7.28/7.26 117 (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]. 7.28/7.26 118 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((all V1x_27_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)),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))),F2_2E0),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,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)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0)))) -> ((all V0x_2E0 all V1x_27_2E0 all V3x_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))),F1_2E0),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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))),s(A_27a,V3x_2E0)))))) -> ((all V1x_27_2E0 all V2x_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))),s(A_27a,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)))) -> (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),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))),F1_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)))))))))) # label(thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 119 (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]. 7.28/7.27 120 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> s(tyop_2Emin_2Ebool,V3y_27_2E0) = s(tyop_2Emin_2Ebool,V2y_2E0)) & s(tyop_2Emin_2Ebool,V1x_27_2E0) = 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_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 121 (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,V1P_27_2E0) = s(tyop_2Emin_2Ebool,V0P_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,V2Q_2E0)) & p(s(tyop_2Emin_2Ebool,V0P_2E0)) <-> p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) & p(s(tyop_2Emin_2Ebool,V1P_27_2E0))))) # label(thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 122 (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]. 7.28/7.27 123 (all A_27a all V0P_2E0 all 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)))) <-> (exists V2x_2E0 (s(A_27a,V1a_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)))))))) # label(thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 124 (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]. 7.28/7.27 125 (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,V1t2_2E0)))) # label(thm_2Ebool_2EOR__INTRO__THM2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 126 (all A_27a all A_27b all V0f_2E0 all 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))) = s(A_27b,app_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]. 7.28/7.27 127 (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__ABS) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 128 (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]. 7.28/7.27 129 (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]. 7.28/7.27 130 (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]. 7.28/7.27 131 (all A_27a all V0P_2E0 all V1Q_2E0 (((all V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) -> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2EBOTH__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 132 (all A_27a all V0P_2E0 all V1Q_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))))) <-> (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)))))))) # label(thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 133 (all A_27a all F0_2E0 ((all V1x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> (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),F0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 134 (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,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)))))) -> ((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,V4x_2E0))),s(A_27a,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)))) -> (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,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))))) = 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))))))))) # label(thm_2Ebool_2ELCOMM__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 135 (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,V0P_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]. 7.28/7.27 136 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2x_2E0 all 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))))) = 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)))))) # label(thm_2Ebool_2ECOND__RAND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 137 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V2t3_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2t3_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2ECONJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 138 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2M_2E0 all V3N_2E0 ((all V4x_2E0 (s(A_27a,V3N_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,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),V1g_2E0),s(A_27a,V3N_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2M_2E0))))) # label(thm_2Ebool_2ELET__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 139 (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]. 7.28/7.27 140 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Ebool_2Eitself__case_2E2(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0),s(A_27b,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)))) # label(arityeq2_2Ec_2Ebool_2Eitself__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 141 (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]. 7.28/7.27 142 (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,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0))))) # label(thm_2Ebool_2EAND__INTRO__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 143 (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]. 7.28/7.27 144 (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]. 7.28/7.27 145 (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)) -> p(s(tyop_2Emin_2Ebool,V0A_2E0))))) # label(thm_2Ebool_2EOR__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 146 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) & s(A_27a,V1y_2E0) = s(A_27a,V2z_2E0) -> s(A_27a,V2z_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 147 (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)))) <-> (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__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 148 (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]. 7.28/7.27 149 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists 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)))))) <-> 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))))))) # label(thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 150 (all A_27a all A_27b all 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)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 151 (all A_27a all A_27b all 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,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),V0x_2E0)))))) # label(thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 152 (all A_27a all V0t_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 153 (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]. 7.28/7.27 154 (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,V1B_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))))) # label(thm_2Ebool_2ELEFT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 155 (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]. 7.28/7.27 156 (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]. 7.28/7.27 157 (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]. 7.28/7.27 158 (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]. 7.28/7.27 159 (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]. 7.28/7.27 160 (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__RATOR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 161 (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]. 7.28/7.27 162 (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]. 7.28/7.27 163 (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,V1t1_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t2_2E0))))) # label(thm_2Ebool_2ECOND__EXPAND__IMP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 164 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V4x_2E0)))) <-> (exists V5x_27_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V5x_27_2E0))) = s(A_27a,V4x_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,V3x_27_27_2E0) = s(A_27b,V2x_27_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]. 7.28/7.27 165 (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,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V2C_2E0)))) # label(thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 166 (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]. 7.28/7.27 167 (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_2EONTO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(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]. 7.28/7.27 168 (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)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27c,c_2Ebool_2ELET_2E2(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]. 7.28/7.27 169 (all A_27a all V0P_2E0 all 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)))) <-> (exists V2x_2E0 (s(A_27a,V1a_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)))))))) # label(thm_2Ebool_2EUNWIND__THM1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 170 (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]. 7.28/7.27 171 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((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,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))),F1_2E0),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)))) -> ((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)),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))),F0_2E0),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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0)))) -> (all V0b_2E0 all V1N_2E0 all 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)),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))),F0_2E0),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_2ELET_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))),F1_2E0),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_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 172 (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__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 173 (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__THM1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 174 (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]. 7.28/7.27 175 (all A_27a all V0t1_2E0 all 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) & 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_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 176 (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,V1B_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V2C_2E0)))) # label(thm_2Ebool_2ERIGHT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 177 (all A_27a all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 178 (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,V0z_2E0)) | p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0)) | p(s(tyop_2Emin_2Ebool,V3w_2E0))))) # label(thm_2Ebool_2EMONO__OR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 179 (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]. 7.28/7.27 180 (all A_27a all F0_2E0 ((all V0x_2E0 all V1y_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_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)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0)))))) -> (all V0x_2E0 s(A_27a,c_2Emin_2E_40_2E1(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)),F0_2E0),s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)))) # label(thm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 181 (all A_27a all F0_2E0 ((all V0P_2E0 all V1x_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)),F0_2E0),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)))) -> (all 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))))) & (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,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4y_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 182 (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]. 7.28/7.27 183 (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__EQ__IMP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 184 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 185 (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]. 7.28/7.27 186 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 187 (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]. 7.28/7.27 188 (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]. 7.28/7.27 189 (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]. 7.28/7.27 190 (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_2EEQ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 191 (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]. 7.28/7.27 192 (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]. 7.28/7.27 193 (all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,V0x_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_27_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]. 7.28/7.27 194 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V0P_2E0 all V1N_2E0 all 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))))) = 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))),F1_2E0),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)))) -> ((all V1N_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0)))) -> (all V0P_2E0 all V1N_2E0 all 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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_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))),F1_2E0),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))))))) # label(thm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 195 (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]. 7.28/7.27 196 (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,V0P_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__OR__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 197 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_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)))))) # label(thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 198 (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]. 7.28/7.27 199 (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]. 7.28/7.27 200 (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]. 7.28/7.27 201 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) <-> (all V1x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 202 (all A_27a all 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))))) <-> -(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_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 203 (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]. 7.28/7.27 204 (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]. 7.28/7.27 205 (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]. 7.28/7.27 206 (all A_27a all X0_2E0 all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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]. 7.28/7.27 207 (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]. 7.28/7.27 208 (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]. 7.28/7.27 209 (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)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,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)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 210 (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,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_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))))) & (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),V4m1_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))))))) # label(thm_2Ebool_2ERES__ABSTRACT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 211 (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]. 7.28/7.27 212 (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]. 7.28/7.27 213 (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 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))))) = s(A_27b,V4a_2E0)) & (all 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) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5r_2E0)))))))))) # label(thm_2Ebool_2EABS__REP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 214 (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]. 7.28/7.27 215 (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]. 7.28/7.27 216 (all A_27a all A_27b all V0M_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 217 (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_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(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]. 7.28/7.27 218 (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]. 7.28/7.27 219 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((all V0P_2E0 all V1N_2E0 all V4x_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))),F1_2E0),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))) = 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)))))) -> ((all V1N_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0)))) -> (all V0P_2E0 all V1N_2E0 all 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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0))))) = s(A_27c,c_2Ebool_2Eliteral__case_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))),F1_2E0),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))))))) # label(thm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 220 (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]. 7.28/7.27 221 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) -> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 222 (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,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_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]. 7.28/7.27 223 (all A_27a all A_27b all V0M_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2EETA__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 224 (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)))) & ((exists V7x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V7x_2E0)))) & p(s(tyop_2Emin_2Ebool,V1Q_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))) & (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 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))))))) # label(thm_2Ebool_2EPULL__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 225 (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]. 7.28/7.27 226 (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]. 7.28/7.27 227 (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]. 7.28/7.27 228 (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]. 7.28/7.27 229 (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))) & (-(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))))) # label(thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 230 (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]. 7.28/7.27 231 (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 232 (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]. 7.28/7.27 233 (all V0x_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Ebool_2ENOT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 234 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((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,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))),F1_2E0),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)))) -> ((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)),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))),F0_2E0),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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0)))) -> (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)),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))),F0_2E0),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),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))),F1_2E0),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]. 7.28/7.27 235 (all A_27a all F0_2E0 ((all V0t_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,V0t_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)),F0_2E0),s(tyop_2Emin_2Ebool,V0t_2E0))),s(A_27a,V1x_2E0)))) -> (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(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)),F0_2E0),s(tyop_2Emin_2Ebool,V0t_2E0)))))) <-> (all V2x_2E0 all V3y_2E0 s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))))) # label(thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 236 (all F3_2E0 all F0_2E0 all F1_2E0 all F2_2E0 ((all V4b_2E0 (-p(s(tyop_2Emin_2Ebool,V4b_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Emin_2Ebool,V4b_2E0)))))) -> ((all V1b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> ((all V2b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Emin_2Ebool,V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> ((all V3b_2E0 s(tyop_2Emin_2Ebool,V3b_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Emin_2Ebool,V3b_2E0)))) -> (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),F0_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),F2_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),F3_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),F1_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]. 7.28/7.27 237 (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)) & (-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)) | p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2EOR__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 238 (all A_27a all F0_2E0 ((all V0x_2E0 all V1x_27_2E0 all 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)))) <-> p(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))),F0_2E0),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)))))) -> (all V0x_2E0 all 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))) = s(A_27a,c_2Emin_2E_40_2E1(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))),F0_2E0),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]. 7.28/7.27 239 (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),V1f_2E0),s(A_27a,V4x_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,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]. 7.28/7.27 240 (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]. 7.28/7.27 241 (all A_27a all V0t1_2E0 all V1t2_2E0 exists V2fn_2E0 (s(A_27a,V0t1_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,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))))) # label(thm_2Ebool_2EboolAxiom) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 242 (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]. 7.28/7.27 243 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0)) | p(s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2EOR__INTRO__THM1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 244 (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]. 7.28/7.27 245 (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]. 7.28/7.27 246 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 (s(tyop_2Emin_2Ebool,V1P_27_2E0) = s(tyop_2Emin_2Ebool,V0P_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,V1P_27_2E0)) | p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,V2Q_2E0))))) # label(thm_2Ebool_2ELEFT__OR__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 247 (all A_27a all F0_2E0 ((all V0P_2E0 all V1f_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(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))),F0_2E0),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)))))) -> (all V0P_2E0 all V1f_2E0 s(A_27a,c_2Emin_2E_40_2E1(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))),F0_2E0),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_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)))))) # label(thm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 248 (all A_27a all A_27b all V0P_2E0 all 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)))) <-> (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,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_27b,V3x_27_27_2E0) = s(A_27b,V2x_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),V1rep_2E0),s(A_27b,V5x_27_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_2Ebool_2ETYPE__DEFINITION__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 249 (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]. 7.28/7.27 250 (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]. 7.28/7.27 251 (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]. 7.28/7.27 252 (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]. 7.28/7.27 253 (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,V1B_2E0)) & p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 254 (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))) & (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,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))))) # label(thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 255 (all V0b_2E0 all V1t1_2E0 all 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)) <-> 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)))))) # label(thm_2Ebool_2ECOND__EXPAND__OR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 256 (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]. 7.28/7.27 257 (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]. 7.28/7.27 258 (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]. 7.28/7.27 259 (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]. 7.28/7.27 260 (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]. 7.28/7.27 261 (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,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_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,V3y_27_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 262 (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]. 7.28/7.27 263 (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]. 7.28/7.27 264 (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__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 265 (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]. 7.28/7.27 266 (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__TX) # label(axiom) # label(non_clause). [assumption]. 7.28/7.27 267 (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),V1P_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_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]. 7.28/7.27 268 (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]. 7.28/7.27 269 (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]. 7.28/7.27 270 (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]. 7.28/7.27 271 (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]. 7.28/7.28 272 (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]. 7.28/7.28 273 (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]. 7.28/7.28 274 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 275 (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]. 7.28/7.28 276 (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]. 7.28/7.28 277 (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]. 7.28/7.28 278 (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]. 7.28/7.28 279 (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]. 7.28/7.28 280 (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]. 7.28/7.28 281 (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]. 7.28/7.28 282 (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]. 7.28/7.28 283 (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,V0x_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__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 284 (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]. 7.28/7.28 285 (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]. 7.28/7.28 286 (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]. 7.28/7.28 287 (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]. 7.28/7.28 288 (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]. 7.28/7.28 289 (all A_27a all V0t1_2E0 all 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_2EConseqConv_2ECOND__CLAUSES__CT) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 290 (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]. 7.28/7.28 291 (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__disj__strengthen) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 292 (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]. 7.28/7.28 293 (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,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,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__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 294 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(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_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)))) # label(arityeq2_2Ec_2EConseqConv_2EASM__MARKER_2E2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 295 (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]. 7.28/7.28 296 (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]. 7.28/7.28 297 (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]. 7.28/7.28 298 (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,V1x_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,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]. 7.28/7.28 299 (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__XT) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 300 (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]. 7.28/7.28 301 (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]. 7.28/7.28 302 (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]. 7.28/7.28 303 (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 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))))) <-> (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)))))))) # label(thm_2EConseqConv_2Eforall__eq__thm) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 304 (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]. 7.28/7.28 305 (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__XT) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 306 (all V0x_2E0 all V1x_27_2E0 s(tyop_2Emin_2Ebool,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)))) # label(thm_2EConseqConv_2EASM__MARKER__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 307 (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]. 7.28/7.28 308 (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]. 7.28/7.28 309 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 310 (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]. 7.28/7.28 311 (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]. 7.28/7.28 312 (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]. 7.28/7.28 313 (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]. 7.28/7.28 314 (all V0c_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,V1x_2E0)) & p(s(tyop_2Emin_2Ebool,V0c_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)))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__FF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 315 (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]. 7.28/7.28 316 (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]. 7.28/7.28 317 (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]. 7.28/7.28 318 (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]. 7.28/7.28 319 (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,V3y_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,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__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 320 (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]. 7.28/7.28 321 (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]. 7.28/7.28 322 (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]. 7.28/7.28 323 (all A_27a all V0x_2E0 s(A_27a,c_2Emarker_2Estmarker_2E1(s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Emarker_2Estmarker__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 324 (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]. 7.28/7.28 325 (all A_27a all X0_2E0 s(A_27a,c_2Emarker_2Eunint_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Emarker_2Eunint_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Eunint_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 326 (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]. 7.28/7.28 327 (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]. 7.28/7.28 328 (all 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))) = s(tyop_2Emin_2Ebool,c_2Emarker_2ECong_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2ECong_2E1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 329 (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,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,V1q_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,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,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0))))) # label(thm_2Emarker_2Emove__right__conj) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 330 (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]. 7.28/7.28 331 (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]. 7.28/7.28 332 (all V0lab_2E0 all V1argument_2E0 s(tyop_2Emin_2Ebool,V1argument_2E0) = s(tyop_2Emin_2Ebool,c_2Emarker_2E_3A_2D_2E2(s(tyop_2Emin_2Eind,V0lab_2E0),s(tyop_2Emin_2Ebool,V1argument_2E0)))) # label(thm_2Emarker_2Elabel__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 333 (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]. 7.28/7.28 334 (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]. 7.28/7.28 335 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2EAC_2E2(s(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_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)))) # label(arityeq2_2Ec_2Emarker_2EAC_2E2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 336 (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]. 7.28/7.28 337 (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]. 7.28/7.28 338 (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]. 7.28/7.28 339 (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]. 7.28/7.28 340 (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]. 7.28/7.28 341 (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2ECong_2E1(s(tyop_2Emin_2Ebool,V0x_2E0))) = s(tyop_2Emin_2Ebool,V0x_2E0)) # label(thm_2Emarker_2ECong__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 342 (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,V0p_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,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,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]. 7.28/7.28 343 (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]. 7.28/7.28 344 (all 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))) = s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 345 (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,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,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))))))) # label(thm_2Emarker_2Emove__left__disj) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 346 (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]. 7.28/7.28 347 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_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_2EAbbrev_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2EAbbrev_2E1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 348 (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]. 7.28/7.28 349 (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]. 7.28/7.28 350 (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]. 7.28/7.28 351 (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]. 7.28/7.28 352 (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]. 7.28/7.28 353 (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,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,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,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]. 7.28/7.28 354 (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]. 7.28/7.28 355 (all V0b1_2E0 all V1b2_2E0 (p(s(tyop_2Emin_2Ebool,V1b2_2E0)) & p(s(tyop_2Emin_2Ebool,V0b1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Emarker_2EAC_2E2(s(tyop_2Emin_2Ebool,V0b1_2E0),s(tyop_2Emin_2Ebool,V1b2_2E0)))))) # label(thm_2Emarker_2EAC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 356 (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]. 7.28/7.28 357 (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]. 7.28/7.28 358 (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]. 7.28/7.28 359 (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]. 7.28/7.28 360 (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]. 7.28/7.28 361 (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]. 7.28/7.28 362 (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]. 7.28/7.28 363 (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]. 7.28/7.28 364 (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) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 365 (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]. 7.28/7.28 366 (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]. 7.28/7.28 367 (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]. 7.28/7.28 368 (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]. 7.28/7.28 369 (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]. 7.28/7.28 370 (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]. 7.28/7.28 371 (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]. 7.28/7.28 372 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2EnormalForms_2EEXT__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 373 (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]. 7.28/7.28 374 (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]. 7.28/7.28 375 (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]. 7.28/7.28 376 (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]. 7.28/7.28 377 (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]. 7.28/7.28 378 (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]. 7.28/7.28 379 (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]. 7.28/7.28 380 (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]. 7.28/7.28 381 (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]. 7.28/7.28 382 (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]. 7.28/7.28 383 (all V0s_2E0 all V1r_2E0 all V2q_2E0 all 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,V3p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0s_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,V2q_2E0))) & (-p(s(tyop_2Emin_2Ebool,V3p_2E0)) | p(s(tyop_2Emin_2Ebool,V1r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2q_2E0))) & (p(s(tyop_2Emin_2Ebool,V3p_2E0)) | -p(s(tyop_2Emin_2Ebool,V1r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2q_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))) = s(tyop_2Emin_2Ebool,V3p_2E0))) # label(thm_2Esat_2Edc__cond) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 384 (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]. 7.28/7.28 385 (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]. 7.28/7.28 386 (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,V0q_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0q_2E0)) | -p(s(tyop_2Emin_2Ebool,V1p_2E0))))) # label(thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 387 (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]. 7.28/7.28 388 (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]. 7.28/7.28 389 (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]. 7.28/7.28 390 (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]. 7.28/7.28 391 (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]. 7.28/7.28 392 (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,V0q_2E0)))) # label(thm_2Esat_2Epth__an2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 393 (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]. 7.28/7.28 394 (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]. 7.28/7.28 395 (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,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))))) # label(thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 396 (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]. 7.28/7.28 397 (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]. 7.28/7.28 398 (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]. 7.28/7.28 399 (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]. 7.28/7.28 400 (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]. 7.28/7.28 401 (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,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,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]. 7.28/7.28 402 (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,V1A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(thm_2Esat_2EOR__DUAL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 403 (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]. 7.28/7.28 404 (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,V0q_2E0)))) # label(thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 405 (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]. 7.28/7.28 406 (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]. 7.28/7.28 407 (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]. 7.28/7.28 408 (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]. 7.28/7.28 409 (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__no1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 410 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 411 (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]. 7.28/7.28 412 (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,V1A_2E0)) | p(s(tyop_2Emin_2Ebool,V0B_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 413 (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]. 7.28/7.28 414 (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]. 7.28/7.28 415 (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]. 7.28/7.28 416 (all V0r_2E0 all V1q_2E0 all 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)) | -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))))) # label(thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 417 (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__an1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 418 (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]. 7.28/7.28 419 (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]. 7.28/7.28 420 (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]. 7.28/7.28 421 (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,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]. 7.28/7.28 422 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((s(tyop_2Emin_2Ebool,V0r_2E0) = 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)) | -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,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 423 (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]. 7.28/7.28 424 (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]. 7.28/7.28 425 (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]. 7.28/7.28 426 (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]. 7.28/7.28 427 (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]. 7.28/7.28 428 (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),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]. 7.28/7.28 429 (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]. 7.28/7.28 430 (all 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))) = 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)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 431 (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_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))) = 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)))))) # label(thm_2Ecombin_2Eo__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 432 (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]. 7.28/7.28 433 (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]. 7.28/7.28 434 (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]. 7.28/7.28 435 (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]. 7.28/7.28 436 (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]. 7.28/7.28 437 (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]. 7.28/7.28 438 (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]. 7.28/7.28 439 (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)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,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)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 440 (all A_27b all A_27c all 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))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 441 (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]. 7.28/7.28 442 (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]. 7.28/7.28 443 (all A_27a all A_27b 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_27b,A_27b)),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,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)))) # label(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 444 (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]. 7.28/7.28 445 (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]. 7.28/7.28 446 (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]. 7.28/7.28 447 (all A_27a all A_27b all A_27d all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 448 (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]. 7.28/7.28 449 (all A_27a all A_27b all F0_2E0 ((all V1a_2E0 all V3c_2E0 (s(A_27a,V3c_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)),F0_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3c_2E0)))))) -> (all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_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)),F0_2E0),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))))) = 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)))))) # label(thm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 450 (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]. 7.28/7.28 451 (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),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,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))) # label(thm_2Ecombin_2EUPDATE__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 452 (all A_27a all A_27b all A_27c all F0_2E0 ((all V0g_2E0 all V3x_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)),F0_2E0),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)))) -> (all V0g_2E0 all V1f_2E0 all 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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_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),V1f_2E0),s(A_27c,app_2E2(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]. 7.28/7.28 453 (all A_27a all A_27b 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_27b,A_27a)),V0f_2E0),s(A_27b,V1e_2E0)))) <-> (all 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))) = s(A_27a,V2x_2E0)))) # label(thm_2Ecombin_2ERIGHT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 454 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Ecombin_2EK__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 455 (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]. 7.28/7.28 456 (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)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,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)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 457 (all A_27a all A_27b all A_27c all F0_2E0 ((all V0g_2E0 all V3x_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)),F0_2E0),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)))) -> (all V0g_2E0 all V1f_2E0 all 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))))) = 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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),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]. 7.28/7.28 458 (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]. 7.28/7.28 459 (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]. 7.28/7.28 460 (all A_27a all 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))) = 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_2EFCOMM__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 461 (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_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))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_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]. 7.28/7.28 462 (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]. 7.28/7.28 463 (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]. 7.28/7.28 464 (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_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))) = 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)))) # label(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 465 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,c_2Ecombin_2EFAIL_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_2EFAIL_2E0),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]. 7.28/7.28 466 (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]. 7.28/7.28 467 (all A_27a all V0f_2E0 all 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_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_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]. 7.28/7.28 468 (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]. 7.28/7.28 469 (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_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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.28 470 (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_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_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)))) # label(thm_2Ecombin_2EGEN__literal__case__RAND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 471 (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]. 7.28/7.29 472 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 473 (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]. 7.28/7.29 474 (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]. 7.28/7.29 475 (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]. 7.28/7.29 476 (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]. 7.28/7.29 477 (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]. 7.28/7.29 478 (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]. 7.28/7.29 479 (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_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,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)))))) # label(thm_2Ecombin_2Eo__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 480 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0)))) # label(thm_2Ecombin_2EFAIL__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 481 (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]. 7.28/7.29 482 (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_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0)))) # label(thm_2Ecombin_2ELET__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 483 (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]. 7.28/7.29 484 (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]. 7.28/7.29 485 (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,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)))))) <-> 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__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 486 (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,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(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)))) # label(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 487 (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]. 7.28/7.29 488 (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]. 7.28/7.29 489 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,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)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 490 (all A_27a all V0v_2E0 all 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))) = 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_2Eliteral__case__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 491 (all A_27a all A_27b all V0f_2E0 all V1a_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,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)))) # label(thm_2Ecombin_2EAPPLY__UPDATE__ID) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 492 (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]. 7.28/7.29 493 (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]. 7.28/7.29 494 (all A_27a all A_27b all A_27c all A_27d ((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)))) & (all V3a_2E0 all V4b_2E0 all V5x_2E0 all V6f_2E0 (s(A_27c,V3a_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))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))))))) # label(thm_2Ecombin_2EUPDATE__APPLY) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 495 (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]. 7.28/7.29 496 (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,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),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)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 497 (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]. 7.28/7.29 498 (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]. 7.28/7.29 499 (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]. 7.28/7.29 500 (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]. 7.28/7.29 501 (all A_27a all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 502 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 503 (all A_27e all A_27f all X0_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,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)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 504 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 505 (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]. 7.28/7.29 506 (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]. 7.28/7.29 507 (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]. 7.28/7.29 508 (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]. 7.28/7.29 509 (all A_27a all A_27b all A_27c all F0_2E0 ((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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27a,V3x_2E0)))) -> (all V0y_2E0 all V1f_2E0 all 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))) = s(A_27b,c_2Ecombin_2EC_2E3(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))),F0_2E0),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)))))) # label(thm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 510 (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]. 7.28/7.29 511 (all A_27a all A_27b all 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))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(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]. 7.28/7.29 512 (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,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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 513 (all A_27a all A_27b all A_27c all F0_2E0 ((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,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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0))),s(A_27a,V3x_2E0)))) -> (all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27c,c_2Ecombin_2Eo_2E3(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)),F0_2E0),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))) = 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)))))))) # label(thm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 514 (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]. 7.28/7.29 515 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all 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))) = 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)))) # label(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 516 (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]. 7.28/7.29 517 (all A_27a all A_27b all A_27c all V0x_2E0 all V1v_2E0 all V2f_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))) = 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)))) # label(thm_2Ecombin_2EGEN__LET__RATOR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 518 (all A_27a all X0_2E0 all 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))) = 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)))) # 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]. 7.28/7.29 519 (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]. 7.28/7.29 520 (all A_27a all A_27b all F0_2E0 ((all V0a_2E0 all V3x_27_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)),F0_2E0),s(A_27a,V0a_2E0))),s(A_27a,V3x_27_2E0)))) <-> s(A_27a,V0a_2E0) = s(A_27a,V3x_27_2E0))) -> (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,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)),F0_2E0),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]. 7.28/7.29 521 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 522 (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]. 7.28/7.29 523 (all A_27a all A_27b all A_27c all X0_2E0 all 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))) = 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)))) # 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]. 7.28/7.29 524 (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]. 7.28/7.29 525 (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,V4b_2E0) != s(A_27d,V5c_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))) != 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))))) # label(thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 526 (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]. 7.28/7.29 527 (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]. 7.28/7.29 528 (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]. 7.28/7.29 529 (all A_27a all A_27b all A_27c all V0x_2E0 all V1x_27_2E0 all 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))) = 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)))) # label(thm_2Ecombin_2EC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 530 (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]. 7.28/7.29 531 (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),V0f_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(A_27b,V3c_2E0) = s(A_27b,V2b_2E0))) # label(thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 532 (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]. 7.28/7.29 533 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,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)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 534 (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,V2y_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,V2y_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]. 7.28/7.29 535 (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]. 7.28/7.29 536 (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]. 7.28/7.29 537 (all A_27a 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_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_2ERIGHT__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_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 538 (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_2ELEFT__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_2ELEFT__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_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 539 (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]. 7.28/7.29 540 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 ((all V2x_2E0 s(A_27b,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)))) <-> 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)))))) # label(thm_2Ecombin_2ELEFT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 541 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 542 (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]. 7.28/7.29 543 (all A_27a all A_27b all A_27c all F0_2E0 ((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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27a,V3x_2E0)))) -> (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)),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))),F0_2E0),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]. 7.28/7.29 544 (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_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,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)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 545 (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),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]. 7.28/7.29 546 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 all V4d_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),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),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))) & 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,V2b_2E0) != s(A_27a,V1a_2E0) | s(A_27a,V1a_2E0) = s(A_27a,V2b_2E0) & s(A_27b,V3c_2E0) = s(A_27b,V4d_2E0))) # label(thm_2Ecombin_2EUPD11__SAME__BASE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 547 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all 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,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_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))) # label(thm_2Ecombin_2EUPDATE__APPLY__ID) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 548 (all A_27a all A_27b all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 549 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 550 (all A_27a all A_27b all V0f_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) & 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),V0f_2E0))) # label(thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 551 (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,V3b_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,V4c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_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),V1f2_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(A_27b,V4c_2E0) = s(A_27b,V3b_2E0))) # label(thm_2Ecombin_2EUPD__SAME__KEY__UNWIND) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 552 (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]. 7.28/7.29 553 (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]. 7.28/7.29 554 (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]. 7.28/7.29 555 (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]. 7.28/7.29 556 (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]. 7.28/7.29 557 (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]. 7.28/7.29 558 (all V0m_2E0 all V1n_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,V0m_2E0))) -> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Enum_2EINV__SUC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 559 (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]. 7.28/7.29 560 (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]. 7.28/7.29 561 (all V0y_2E0 s(tyop_2Emin_2Eind,c_2Enum_2EZERO__REP_2E0) != s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,V0y_2E0)))) # label(thm_2Enum_2EZERO__REP__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 562 (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]. 7.28/7.29 563 (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]. 7.28/7.29 564 (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]. 7.28/7.29 565 (all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 566 (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]. 7.28/7.29 567 (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]. 7.28/7.29 568 (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]. 7.28/7.29 569 (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]. 7.28/7.29 570 (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]. 7.28/7.29 571 (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]. 7.28/7.29 572 (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]. 7.28/7.29 573 (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]. 7.28/7.29 574 (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]. 7.28/7.29 575 (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_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 576 (all V0a_2E0 s(tyop_2Enum_2Enum,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)))))) # label(thm_2Enum_2Enum__ISO__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 577 (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]. 7.28/7.29 578 (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]. 7.28/7.29 579 (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]. 7.28/7.29 580 (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]. 7.28/7.29 581 (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]. 7.28/7.29 582 (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]. 7.28/7.29 583 (all 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)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,V0m_2E0)))))) # label(thm_2Enum_2EIS__NUM__REP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 584 (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]. 7.28/7.29 585 (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]. 7.28/7.29 586 (all 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))) = s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EIS__NUM__REP_2E1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 587 (all 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))) = s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC__REP_2E1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 588 (all V0P_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)))))))) & 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 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]. 7.28/7.29 589 (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]. 7.28/7.29 590 (all 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))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Enum_2ESUC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 591 (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]. 7.28/7.29 592 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(A_27a,V0x_2E0)))) # label(thm_2Eone_2Eone__case__thm) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 593 (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]. 7.28/7.29 594 (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]. 7.28/7.29 595 (all F0_2E0 ((all V1b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))) = s(tyop_2Emin_2Ebool,V1b_2E0)) -> (exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_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]. 7.28/7.29 596 (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]. 7.28/7.29 597 (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]. 7.28/7.29 598 (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]. 7.28/7.29 599 (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]. 7.28/7.29 600 (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]. 7.28/7.29 601 (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]. 7.28/7.29 602 (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]. 7.28/7.29 603 (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]. 7.28/7.29 604 (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]. 7.28/7.29 605 (all F0_2E0 ((all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eone_2Eone,V0x_2E0)))) -> s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0) = s(tyop_2Eone_2Eone,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),F0_2E0))))) # label(thm_2Eone_2Eone__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 606 (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]. 7.28/7.29 607 (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]. 7.28/7.29 608 (all A_27a all V0u_2E0 all V1x_2E0 s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,V0u_2E0),s(A_27a,V1x_2E0))) = s(A_27a,V1x_2E0)) # label(thm_2Eone_2Eone__case__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 609 (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]. 7.28/7.29 610 (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]. 7.28/7.29 611 (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]. 7.28/7.29 612 (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]. 7.28/7.29 613 (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_2EFORALL__ONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 614 (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]. 7.28/7.29 615 (all A_27a all V0e_2E0 exists 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(thm_2Eone_2Eone__prim__rec) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 616 (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]. 7.28/7.29 617 (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]. 7.28/7.29 618 (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]. 7.28/7.29 619 (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]. 7.28/7.29 620 (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]. 7.28/7.29 621 (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]. 7.28/7.29 622 (all A_27a all F0_2E0 ((all V0e_2E0 all 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) <-> p(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)),F0_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0)))))) -> (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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0e_2E0))))))))) # label(thm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 623 (all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 624 (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]. 7.28/7.29 625 (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]. 7.28/7.29 626 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all 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))) = 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)))) # label(arityeq4_2Ec_2Erelation_2ERUNION_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 627 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_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 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)))))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.29 628 (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]. 7.28/7.29 629 (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]. 7.28/7.29 630 (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]. 7.28/7.30 631 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all 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))) = 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)))) # label(arityeq4_2Ec_2Erelation_2Einv__image_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 632 (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]. 7.28/7.30 633 (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_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(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)))) # label(arityeq2_2Ec_2Erelation_2ERRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 634 (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]. 7.28/7.30 635 (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]. 7.28/7.30 636 (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,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))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))))) # label(thm_2Erelation_2ERESTRICT__LEMMA) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 637 (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]. 7.28/7.30 638 (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]. 7.28/7.30 639 (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]. 7.28/7.30 640 (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]. 7.28/7.30 641 (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_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)))))) # label(thm_2Erelation_2Einv__RC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 642 (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]. 7.28/7.30 643 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all 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)))) <-> -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_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 644 (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]. 7.28/7.30 645 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all 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))) = 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)))) # label(arityeq4_2Ec_2Erelation_2ERDOM__DELETE_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 646 (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_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_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]. 7.28/7.30 647 (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_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)))))) # label(thm_2Erelation_2Ereflexive__inv) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 648 (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]. 7.28/7.30 649 (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)))) & 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_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]. 7.28/7.30 650 (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]. 7.28/7.30 651 (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,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_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]. 7.28/7.30 652 (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]. 7.28/7.30 653 (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,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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2EWFP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 654 (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]. 7.28/7.30 655 (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]. 7.28/7.30 656 (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)))))))) <-> 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)))))) & s(A_27a,V1k_2E0) != s(A_27a,V0x_2E0))) # label(thm_2Erelation_2EIN__RDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 657 (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)),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_2ERTC_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]. 7.28/7.30 658 (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]. 7.28/7.30 659 (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]. 7.28/7.30 660 (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 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,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,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,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 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]. 7.28/7.30 661 (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]. 7.28/7.30 662 (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]. 7.28/7.30 663 (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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 664 (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)),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)))))))) <-> 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)),V2R_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM__RRESTRICT) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 665 (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]. 7.28/7.30 666 (all A_27a all V0R_2E0 all V1P_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 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__INDUCT) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 667 (all A_27a all V0R_2E0 all V1P_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,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)),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]. 7.28/7.30 668 (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]. 7.28/7.30 669 (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,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_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]. 7.28/7.30 670 (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)),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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 671 (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]. 7.28/7.30 672 (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_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 673 (all A_27z all 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))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(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]. 7.28/7.30 674 (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,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,V2y_2E0) = s(A_27a,V1x_2E0))) # label(thm_2Erelation_2ERTC__CASES1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 675 (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 ((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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V3min_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]. 7.28/7.30 676 (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]. 7.28/7.30 677 (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_2Etrichotomous_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Etrichotomous_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 678 (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]. 7.28/7.30 679 (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]. 7.28/7.30 680 (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_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__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,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]. 7.28/7.30 681 (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]. 7.28/7.30 682 (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_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_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_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]. 7.28/7.30 683 (all A_27a all 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))) = 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)))) # 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]. 7.28/7.30 684 (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)),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_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)))) # label(thm_2Erelation_2ERUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 685 (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]. 7.28/7.30 686 (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]. 7.28/7.30 687 (all A_27a all A_27b all F0_2E0 ((all V1M_2E0 all V0R_2E0 all V2f_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)),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))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0)))) <-> p(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))),F0_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(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))))) -> (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),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))),F0_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))))))))))) # label(thm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 688 (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]. 7.28/7.30 689 (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]. 7.28/7.30 690 (all A_27a all V0R_2E0 all V1a_2E0 all 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)))) <-> (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,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,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,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)))))))) # label(thm_2Erelation_2ETC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 691 (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]. 7.28/7.30 692 (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]. 7.28/7.30 693 (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]. 7.28/7.30 694 (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)),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)))))) # label(thm_2Erelation_2Eirreflexive__inv) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 695 (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]. 7.28/7.30 696 (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]. 7.28/7.30 697 (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]. 7.28/7.30 698 (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,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,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)),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__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 699 (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)),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_2Ereflexive__RC__identity) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 700 (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]. 7.28/7.30 701 (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]. 7.28/7.30 702 (all A_27a 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))) = 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]. 7.28/7.30 703 (all A_27a all V0R_2E0 all V1P_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)),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)),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,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__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 704 (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]. 7.28/7.30 705 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all 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)))) <-> 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)))))) # label(thm_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 706 (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 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)))) # label(thm_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 707 (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]. 7.28/7.30 708 (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]. 7.28/7.30 709 (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]. 7.28/7.30 710 (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]. 7.28/7.30 711 (all A_27a all 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)))) & 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_2ELinearOrder_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]. 7.28/7.30 712 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2P_2E0 all V3M_2E0 all 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)),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,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_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,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]. 7.28/7.30 713 (all A_27a all 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_2EEMPTY__REL_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))))) & 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)))))) # label(thm_2Erelation_2EREMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 714 (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),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)))) -> 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]. 7.28/7.30 715 (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]. 7.28/7.30 716 (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]. 7.28/7.30 717 (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,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,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,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__STRONG__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 718 (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,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 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]. 7.28/7.30 719 (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]. 7.28/7.30 720 (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]. 7.28/7.30 721 (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]. 7.28/7.30 722 (all A_27a all A_27b all F0_2E0 ((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,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)))),F0_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,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)))) -> (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),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)))),F0_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,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]. 7.28/7.30 723 (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)))) <-> (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)))))) # label(thm_2Erelation_2Esymmetric__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 724 (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)),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_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)))) # label(thm_2Erelation_2ERINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 725 (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_2Ediamond_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Ediamond_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 726 (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]. 7.28/7.30 727 (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]. 7.28/7.30 728 (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]. 7.28/7.30 729 (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)),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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 730 (all A_27a all 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_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_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_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))))) & 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_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_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_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]. 7.28/7.30 731 (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,V1a_2E0) = s(A_27z,V2b_2E0))))) # label(thm_2Erelation_2EINVOL__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 732 (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)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0)))) # label(thm_2Erelation_2ERUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 733 (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)),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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.30 734 (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]. 7.28/7.30 735 (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,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 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]. 7.28/7.31 736 (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_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_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_2ERTC__TC__RC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 737 (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]. 7.28/7.31 738 (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_2EWF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 739 (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]. 7.28/7.31 740 (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]. 7.28/7.31 741 (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]. 7.28/7.31 742 (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)),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)),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)),V1P_2E0)))))) # label(thm_2Erelation_2EWF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 743 (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]. 7.28/7.31 744 (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]. 7.28/7.31 745 (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_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(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)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 746 (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]. 7.28/7.31 747 (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_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_2EWeakLinearOrder_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]. 7.28/7.31 748 (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,V1x_2E0) != s(A_27a,V2y_2E0)))) # label(thm_2Erelation_2EWF__NOT__REFL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 749 (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_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_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_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]. 7.28/7.31 750 (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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 751 (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)),V1R2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0))) # label(thm_2Erelation_2ERSUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 752 (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]. 7.28/7.31 753 (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]. 7.28/7.31 754 (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]. 7.28/7.31 755 (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]. 7.28/7.31 756 (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)),V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),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)))) <-> 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))) # label(thm_2Erelation_2EEqIsBothRSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 757 (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]. 7.28/7.31 758 (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_2ESN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2ESN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 759 (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),V1Q_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,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,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]. 7.28/7.31 760 (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]. 7.28/7.31 761 (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]. 7.28/7.31 762 (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]. 7.28/7.31 763 (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]. 7.28/7.31 764 (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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 765 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2ESC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 766 (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]. 7.28/7.31 767 (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]. 7.28/7.31 768 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 769 (all A_27a all V0R_2E0 all 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)))) <-> (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)))))))) # label(thm_2Erelation_2EWFP__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 770 (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]. 7.28/7.31 771 (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]. 7.28/7.31 772 (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]. 7.28/7.31 773 (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]. 7.28/7.31 774 (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]. 7.28/7.31 775 (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]. 7.28/7.31 776 (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_2ERCOMPL_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_2ERCOMPL_2E1(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]. 7.28/7.31 777 (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]. 7.28/7.31 778 (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]. 7.28/7.31 779 (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]. 7.28/7.31 780 (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_2Enf_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2Enf__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 781 (all A_27a all 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)),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)))))) # label(thm_2Erelation_2ESTRORD__AND__NOT__Id) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 782 (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]. 7.28/7.31 783 (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_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,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_2ETC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 784 (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]. 7.28/7.31 785 (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]. 7.28/7.31 786 (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)),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_2Esymmetric_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]. 7.28/7.31 787 (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]. 7.28/7.31 788 (all A_27a all V0A_2E0 all V1x_2E0 all V2y_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)))) <-> 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)))) & s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))) # label(thm_2Erelation_2Ediag__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 789 (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]. 7.28/7.31 790 (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]. 7.28/7.31 791 (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,V1x_2E0))),s(A_27a,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,V2z_2E0)))))) # label(thm_2Erelation_2ETC__CASES1__E) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 792 (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)),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))) = 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)))))) # label(thm_2Erelation_2ERUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 793 (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 V3P_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))))) & (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)))))) -> 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)))))))) # label(thm_2Erelation_2ERTC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 794 (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,V1x_2E0) != s(A_27a,V0y_2E0)))) # label(thm_2Erelation_2EWF__noloops) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 795 (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_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 796 (all A_27a all A_27b all F0_2E0 ((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)),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)))),F0_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(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0))),s(A_27a,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)))) -> (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)),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)))),F0_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(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]. 7.28/7.31 797 (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]. 7.28/7.31 798 (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]. 7.28/7.31 799 (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_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 800 (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]. 7.28/7.31 801 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERRANGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 802 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 803 (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]. 7.28/7.31 804 (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)),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(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]. 7.28/7.31 805 (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(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))) = 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)))) # label(arityeq4_2Ec_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 806 (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]. 7.28/7.31 807 (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_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__IDEM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 808 (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]. 7.28/7.31 809 (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]. 7.28/7.31 810 (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_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))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)) # label(thm_2Erelation_2EO__Id) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 811 (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]. 7.28/7.31 812 (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]. 7.28/7.31 813 (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]. 7.28/7.31 814 (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]. 7.28/7.31 815 (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]. 7.28/7.31 816 (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,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,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__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 817 (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]. 7.28/7.31 818 (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,V1x_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,V2z_2E0)))))))) # label(thm_2Erelation_2EEXTEND__RTC__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 819 (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]. 7.28/7.31 820 (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,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,V1a_2E0) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V2b_2E0))))))) # label(thm_2Erelation_2EINVOL__ONE__ENO) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 821 (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]. 7.28/7.31 822 (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]. 7.28/7.31 823 (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]. 7.28/7.31 824 (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_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))))) = 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)))))) # label(thm_2Erelation_2Einv__O) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 825 (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_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 826 (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]. 7.28/7.31 827 (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]. 7.28/7.31 828 (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]. 7.28/7.31 829 (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]. 7.28/7.31 830 (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]. 7.28/7.31 831 (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]. 7.28/7.31 832 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2Ercdiamond_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 833 (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]. 7.28/7.31 834 (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)))) | 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]. 7.28/7.31 835 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2ELinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 836 (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]. 7.28/7.31 837 (all A_27a all V0z_2E0 all V1x_2E0 all V2R_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,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,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)))))) # label(thm_2Erelation_2ETC__CASES1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 838 (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_2ESTRORD_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]. 7.28/7.31 839 (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]. 7.28/7.31 840 (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,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))) = 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)))) # label(arityeq4_2Ec_2Erelation_2EO_2E4_2Emono_2EA_27g_20mono_2EA_27h_20mono_2EA_27k) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 841 (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]. 7.28/7.31 842 (all A_27a all A_27b all 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))) = 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)))) # 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]. 7.28/7.31 843 (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]. 7.28/7.31 844 (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]. 7.28/7.31 845 (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)),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))))))) & (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))))))))) # label(thm_2Erelation_2Eantisymmetric__RINTER) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 846 (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]. 7.28/7.31 847 (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_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 848 (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)),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)),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]. 7.28/7.31 849 (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]. 7.28/7.31 850 (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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 851 (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 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(A_27a,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_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]. 7.28/7.31 852 (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]. 7.28/7.31 853 (all A_27a all 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_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_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]. 7.28/7.31 854 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all 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))) = 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)))) # label(arityeq4_2Ec_2Erelation_2ERINTER_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 855 (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]. 7.28/7.31 856 (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]. 7.28/7.31 857 (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]. 7.28/7.31 858 (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]. 7.28/7.31 859 (all A_27a all A_27b all F0_2E0 ((all V0R_2E0 all V1M_2E0 all V2x_2E0 all V3f_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)))),F0_2E0),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)))) -> (all V0R_2E0 all V1M_2E0 all 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),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)))),F0_2E0),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_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)))))) # label(thm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 860 (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]. 7.28/7.31 861 (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]. 7.28/7.31 862 (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_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 863 (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]. 7.28/7.31 864 (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]. 7.28/7.31 865 (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)))) & 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]. 7.28/7.31 866 (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]. 7.28/7.31 867 (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]. 7.28/7.31 868 (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_2Eequivalence_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2Eequivalence_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 869 (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,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)))))) <-> 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]. 7.28/7.31 870 (all A_27a 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,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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 871 (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,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))) = 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.28/7.31 872 (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]. 7.28/7.32 873 (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]. 7.28/7.32 874 (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)),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))))) = 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)))) # label(thm_2Erelation_2ERINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 875 (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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 876 (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)))) & s(A_27a,V2b_2E0) != s(A_27a,V1a_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]. 7.28/7.32 877 (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]. 7.28/7.32 878 (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_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(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)))) # label(arityeq1_2Ec_2Erelation_2Ediag_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 879 (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),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)),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 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]. 7.28/7.32 880 (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]. 7.28/7.32 881 (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]. 7.28/7.32 882 (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]. 7.28/7.32 883 (all A_27a all A_27b all V0y_2E0 all V1R_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)))))) <-> (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))))))) # label(thm_2Erelation_2EIN__RRANGE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 884 (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]. 7.28/7.32 885 (all A_27a all 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))) = 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)))))) # label(thm_2Erelation_2ECR__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 886 (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]. 7.28/7.32 887 (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]. 7.28/7.32 888 (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_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]. 7.28/7.32 889 (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]. 7.28/7.32 890 (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]. 7.28/7.32 891 (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]. 7.28/7.32 892 (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]. 7.28/7.32 893 (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]. 7.28/7.32 894 (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]. 7.28/7.32 895 (all A_27g all 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)))) & 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_2EStrongOrder_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]. 7.28/7.32 896 (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_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,V5y_2E0)))))))) # label(thm_2Erelation_2ERC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 897 (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]. 7.28/7.32 898 (all A_27a all A_27b all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Erelation_2EINDUCTIVE__INVARIANT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 899 (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]. 7.28/7.32 900 (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]. 7.28/7.32 901 (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]. 7.28/7.32 902 (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_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))))) = 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)))) # label(thm_2Erelation_2EO__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 903 (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,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,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,V2x_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Erelation_2ERTC__RULES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 904 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNIV_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))) # label(thm_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 905 (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]. 7.28/7.32 906 (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]. 7.28/7.32 907 (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]. 7.28/7.32 908 (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]. 7.28/7.32 909 (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]. 7.28/7.32 910 (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,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,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_2ETC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 911 (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_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))) & 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))))))) # label(thm_2Erelation_2Einv__SC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 912 (all A_27a all V0R_2E0 all V1a_2E0 all 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),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,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)))))) <-> 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__ALT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 913 (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]. 7.28/7.32 914 (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]. 7.28/7.32 915 (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_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)))) & 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_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Ercdiamond__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 916 (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]. 7.28/7.32 917 (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]. 7.28/7.32 918 (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,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,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,V0z_2E0)))))) # label(thm_2Erelation_2ETC__CASES2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 919 (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_2ECR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2ECR_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 920 (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,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))) = 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)))))) # label(thm_2Erelation_2EWFREC__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 921 (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]. 7.28/7.32 922 (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]. 7.28/7.32 923 (all A_27a all A_27b all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Erelation_2Einv_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 924 (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]. 7.28/7.32 925 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Erelation_2EEQC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 926 (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]. 7.28/7.32 927 (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_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 928 (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_2ERC_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__RC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 929 (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]. 7.28/7.32 930 (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]. 7.28/7.32 931 (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_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]. 7.28/7.32 932 (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_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))) = 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)))) # 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]. 7.28/7.32 933 (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]. 7.28/7.32 934 (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)))) <-> s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2EI_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))))) # label(thm_2Erelation_2EINVOL__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 935 (all A_27a all A_27b all V0R_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_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)))))) # label(thm_2Erelation_2ERDOM__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 936 (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)),c_2Erelation_2EEMPTY__REL_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EEMPTY__REL_2E2(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]. 7.28/7.32 937 (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)),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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 938 (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)))) <-> 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(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))))) <-> 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)))))) # label(thm_2Erelation_2EALT__equivalence) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 939 (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]. 7.28/7.32 940 (all A_27g all A_27h all A_27k all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3z_2E0 ((exists 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)))) & 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,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)))))) # label(thm_2Erelation_2EO__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 941 (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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNIV_2E2(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]. 7.28/7.32 942 (all A_27z all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(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_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0))))) # label(thm_2Erelation_2EIDEM__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 943 (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_2EWF__EQ__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 944 (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)))) <-> (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,V2b_2E0))),s(A_27a,V1a_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,V1a_2E0))),s(A_27a,V2b_2E0)))))))) # label(thm_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 945 (all A_27a all V0R_2E0 all V1P_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,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)),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]. 7.28/7.32 946 (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_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 947 (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_2EOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 948 (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]. 7.28/7.32 949 (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]. 7.28/7.32 950 (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,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)))) -> 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]. 7.28/7.32 951 (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]. 7.28/7.32 952 (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]. 7.28/7.32 953 (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,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_2ERTC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 954 (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]. 7.28/7.32 955 (all A_27a all V0R_2E0 ((all V2x_2E0 all V3y_2E0 all 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,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,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__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 956 (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]. 7.28/7.32 957 (all A_27a all V0R_2E0 all V1a_2E0 all 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),V3Q_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),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)))))) <-> 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__ALT__RIGHT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 958 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2ERRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 959 (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_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)))))) # label(thm_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 960 (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]. 7.28/7.32 961 (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]. 7.28/7.32 962 (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_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_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_2Eequivalence_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]. 7.28/7.32 963 (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]. 7.28/7.32 964 (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_2EWCR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EWCR_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 965 (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)))) -> 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)))) | (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)))))))) # label(thm_2Erelation_2ETC__CASES2__E) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 966 (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]. 7.28/7.32 967 (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]. 7.28/7.32 968 (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]. 7.28/7.32 969 (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_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_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))))) # label(thm_2Erelation_2Einv__EQC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 970 (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]. 7.28/7.32 971 (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]. 7.28/7.32 972 (all A_27a all A_27b all V0R_2E0 all V1s_2E0 all V2x_2E0 all V3y_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)))) <-> 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,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)))))) # label(thm_2Erelation_2ERRESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 973 (all A_27a all 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))) = 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__Id__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 974 (all A_27a all V0P_2E0 all V1R_2E0 ((all V2x_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)))) & (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,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]. 7.28/7.32 975 (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]. 7.28/7.32 976 (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]. 7.28/7.32 977 (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 (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,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)))))))) # label(thm_2Erelation_2EWeakOrder__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 978 (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]. 7.28/7.32 979 (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]. 7.28/7.32 980 (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]. 7.28/7.32 981 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2u_2E0 all V3v_2E0 (s(A_27a,V2u_2E0) != s(A_27a,V1x_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)))) <-> 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)))))) # label(thm_2Erelation_2ERDOM__DELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 982 (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]. 7.28/7.32 983 (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_2ERC_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_2ERC_2E1(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]. 7.28/7.32 984 (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]. 7.28/7.32 985 (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]. 7.28/7.32 986 (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]. 7.28/7.32 987 (all A_27g all 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)))) <-> 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_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_2Etransitive_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]. 7.28/7.32 988 (all A_27a all V0a_2E0 all V1R_2E0 all V2Q_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 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 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]. 7.28/7.32 989 (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]. 7.28/7.32 990 (all A_27a all 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))))) = 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_2ESTRORD__Strong) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 991 (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]. 7.28/7.32 992 (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]. 7.28/7.32 993 (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]. 7.28/7.32 994 (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_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__EQN) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 995 (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]. 7.28/7.32 996 (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]. 7.28/7.32 997 (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)))) <-> (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,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)))))))))) # label(thm_2Erelation_2Ediamond__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 998 (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]. 7.28/7.32 999 (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]. 7.28/7.32 1000 (all A_27a all A_27b all X0_2E0 s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),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)))) # label(arityeq1_2Ec_2Esum_2EOUTL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 1001 (all A_27a all A_27b all V0ss_2E0 ((exists V2y_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),V0ss_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_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)))))) # label(thm_2Esum_2Esum__CASES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 1002 (all A_27a all A_27b all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 1003 (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]. 7.28/7.32 1004 (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_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))) = 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)))))) # label(thm_2Esum_2ESUM__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.32 1005 (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)),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))) = 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)))) # 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]. 7.28/7.32 1006 (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),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))) = 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)))) # 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]. 7.28/7.32 1007 (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]. 7.28/7.32 1008 (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]. 7.28/7.32 1009 (all A_27a all A_27b all 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))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINL_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1010 (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]. 7.28/7.33 1011 (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]. 7.28/7.33 1012 (all A_27a all A_27b all A_27c all X0_2E0 all 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))) = 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)))) # 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]. 7.28/7.33 1013 (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]. 7.28/7.33 1014 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 exists V2h_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)))) & (all 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))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Esum_2Esum__Axiom) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1015 (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]. 7.28/7.33 1016 (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]. 7.28/7.33 1017 (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]. 7.28/7.33 1018 (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]. 7.28/7.33 1019 (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),c_2Esum_2EINR_2E1(s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))) # label(thm_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1020 (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]. 7.28/7.33 1021 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),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)))) # label(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1022 (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),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))))))) # label(thm_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1023 (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]. 7.28/7.33 1024 (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]. 7.28/7.33 1025 (all A_27a all A_27b ((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))))))) & (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))))))))) # label(thm_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1026 (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]. 7.28/7.33 1027 (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]. 7.28/7.33 1028 (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]. 7.28/7.33 1029 (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]. 7.28/7.33 1030 (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 V4x_2E0 all V5y_2E0 all V6z_2E0 (s(A_27d,V6z_2E0) = s(A_27d,V5y_2E0) & -p(s(tyop_2Emin_2Ebool,V0P_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))))))) & (all V10x_2E0 all V11y_2E0 all V12z_2E0 (s(A_27h,V11y_2E0) = s(A_27h,V12z_2E0) & -p(s(tyop_2Emin_2Ebool,V0P_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))))) & (all V7x_2E0 all V8y_2E0 all V9z_2E0 (s(A_27e,V7x_2E0) = s(A_27e,V9z_2E0) & p(s(tyop_2Emin_2Ebool,V0P_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))))))) & (all V1x_2E0 all V2y_2E0 all V3z_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V3z_2E0) & p(s(tyop_2Emin_2Ebool,V0P_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))))))) # label(thm_2Esum_2Econd__sum__expand) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1031 (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]. 7.28/7.33 1032 (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(A_27a,V0y_2E0) = s(A_27a,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))))))) # label(thm_2Esum_2EINR__INL__11) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1033 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Esum_2EABS__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1034 (all A_27g all A_27h all 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))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1035 (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]. 7.28/7.33 1036 (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(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))) = 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)))) # label(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1037 (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]. 7.28/7.33 1038 (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]. 7.28/7.33 1039 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),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)))) # label(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1040 (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]. 7.28/7.33 1041 (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]. 7.28/7.33 1042 (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]. 7.28/7.33 1043 (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]. 7.28/7.33 1044 (all A_27a all A_27b all V0P_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 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 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]. 7.28/7.33 1045 (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]. 7.28/7.33 1046 (all A_27a all A_27b all A_27c ((all V3y_2E0 all V4f_2E0 all V5f1_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))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0),s(A_27b,V3y_2E0)))) & (all V0x_2E0 all V1f_2E0 all V2f1_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))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Esum_2Esum__case__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1047 (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 (s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_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),V4Q_2E0),s(A_27b,V7b_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(A_27b,V7b_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),V2P_2E0),s(A_27a,V6a_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,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]. 7.28/7.33 1048 (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]. 7.28/7.33 1049 (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]. 7.28/7.33 1050 (all A_27a all A_27b all V0P_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))))) <-> (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))))))))) # label(thm_2Esum_2EEXISTS__SUM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1051 (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]. 7.28/7.33 1052 (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]. 7.28/7.33 1053 (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]. 7.28/7.33 1054 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,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)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1055 (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]. 7.28/7.33 1056 (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__ISL__ISR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1057 (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]. 7.28/7.33 1058 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V0y_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))))) # label(thm_2Esum_2EINL__11) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1059 (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]. 7.28/7.33 1060 (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(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),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)))) # 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]. 7.28/7.33 1061 (all A_27a all A_27b all V0x_2E0 s(A_27a,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)))))) # label(thm_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1062 (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]. 7.28/7.33 1063 (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)),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))) = 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)))) # 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]. 7.28/7.33 1064 (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,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))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V5y_2E0)))))) # label(thm_2Esum_2ESUM__ALL__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1065 (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]. 7.28/7.33 1066 (all A_27a all A_27b all V0f_2E0 ((exists V1v1_2E0 exists V2v2_2E0 ((all V6x_2E0 all V7x_27_2E0 all V8x_27_27_2E0 (s(A_27b,V8x_27_27_2E0) = s(A_27b,V2v2_2E0) & -p(s(tyop_2Emin_2Ebool,V6x_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)))))) | (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)))) <-> p(s(tyop_2Emin_2Ebool,V3x_2E0)) & s(A_27a,V4x_27_2E0) = s(A_27a,V1v1_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]. 7.28/7.33 1067 (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]. 7.28/7.33 1068 (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]. 7.28/7.33 1069 (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))),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))))) <-> 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),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))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V0a_2E0)))) # label(thm_2Esum_2Esum__ISO__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1070 (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))),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))) = 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)))) # label(arityeq1_2Ec_2Esum_2EREP__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1071 (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]. 7.28/7.33 1072 (all A_27a all A_27b all F0_2E0 ((all V0e_2E0 all V1b_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)),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)))),F0_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Ebool,V1b_2E0))),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) <-> s(A_27a,V0e_2E0) = s(A_27a,V2x_2E0) & p(s(tyop_2Emin_2Ebool,V1b_2E0)))) -> (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))),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)))),F0_2E0),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]. 7.28/7.33 1073 (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_2EISL__OR__ISR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1074 (all A_27a all A_27b all A_27c all A_27d ((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)))))) & (all V3f_2E0 all V4g_2E0 all 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))))) = 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)))))))) # label(thm_2Esum_2ESUM__MAP__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1075 (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]. 7.28/7.33 1076 (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]. 7.28/7.33 1077 (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]. 7.28/7.33 1078 (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)),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))) = 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)))) # 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]. 7.28/7.33 1079 (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]. 7.28/7.33 1080 (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]. 7.28/7.33 1081 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,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)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1082 (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]. 7.28/7.33 1083 (all A_27a all A_27b all F0_2E0 ((all V0e_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (s(A_27b,V3y_2E0) = s(A_27b,V0e_2E0) & -p(s(tyop_2Emin_2Ebool,V1b_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))),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)))),F0_2E0),s(A_27b,V0e_2E0))),s(tyop_2Emin_2Ebool,V1b_2E0))),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))))) -> (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))),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)))),F0_2E0),s(A_27b,V0e_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0e_2E0)))))) # label(thm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1084 (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]. 7.28/7.33 1085 (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 (s(tyop_2Esum_2Esum(A_27a,A_27b),V2M_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) & (all V7y_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V7y_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_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),V1f_27_2E0),s(A_27a,V6x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(A_27a,V6x_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]. 7.28/7.33 1086 (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]. 7.28/7.33 1087 (all A_27a all A_27b all V0x_2E0 s(A_27b,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)))))) # label(thm_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1088 (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]. 7.28/7.33 1089 (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]. 7.28/7.33 1090 (all A_27a all A_27b all A_27c all F0_2E0 ((all V0f_2E0 all V1g_2E0 all V2h_2E0 (p(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))),F0_2E0),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_27b,A_27c),V1g_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_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_27a,A_27c),V0f_2E0))) -> (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),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))),F0_2E0),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]. 7.28/7.33 1091 (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]. 7.28/7.33 1092 (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]. 7.28/7.33 1093 (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]. 7.28/7.33 1094 (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]. 7.28/7.33 1095 (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_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))))) = 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)))) # label(thm_2Eoption_2EOPTION__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1096 (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]. 7.28/7.33 1097 (all A_27a all A_27b all X0_2E0 all 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))) = 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)))) # 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]. 7.28/7.33 1098 (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),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2ENOT__IS__SOME__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1099 (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]. 7.28/7.33 1100 (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]. 7.28/7.33 1101 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1102 (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)),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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1103 (all A_27a all V0m2_2E0 all V1m1_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_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),V0m2_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))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__CHOICE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1104 (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)),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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1105 (all A_27a all 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))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(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]. 7.28/7.33 1106 (all A_27a all A_27b all V0x_2E0 all 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))) = 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)))))) # label(thm_2Eoption_2EOPTION__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1107 (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]. 7.28/7.33 1108 (all A_27a all A_27c 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_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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1109 (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]. 7.28/7.33 1110 (all A_27a all V0x_2E0 all V1y_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))))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_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))))) # label(thm_2Eoption_2EOPTION__JOIN__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1111 (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]. 7.28/7.33 1112 (all A_27a all A_27b all V0opt1_2E0 all V1opt2_2E0 all V2f1_2E0 all V3f2_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),V3f2_2E0),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(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1opt2_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]. 7.28/7.33 1113 (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,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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1114 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),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)))) # label(arityeq1_2Ec_2Eoption_2Eoption__REP_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1115 (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]. 7.28/7.33 1116 (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]. 7.28/7.33 1117 (all A_27b all X0_2E0 s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),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)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1118 (all A_27a all F0_2E0 ((all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1x_2E0)))) -> (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),F0_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]. 7.28/7.33 1119 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1120 (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]. 7.28/7.33 1121 (all A_27a all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__CHOICE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1122 (all A_27a all 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))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(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]. 7.28/7.33 1123 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) <-> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0))) # label(thm_2Eoption_2ESOME__11) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1124 (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]. 7.28/7.33 1125 (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]. 7.28/7.33 1126 (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]. 7.28/7.33 1127 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3x0_2E0 exists 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_2ESOME_2E1(s(A_27b,V4y0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),V2y_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),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]. 7.28/7.33 1128 (all A_27a all A_27b ((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)))) & (all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_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)))))) # label(thm_2Eoption_2EOPTION__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1129 (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)))))) -> 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)))) & (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))))) | (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)))))))))) # label(thm_2Eoption_2Esome__elim) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1130 (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]. 7.28/7.33 1131 (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]. 7.28/7.33 1132 (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]. 7.28/7.33 1133 (all A_27a all V0opt_2E0 all V1opt_27_2E0 all V2P_2E0 all V3P_27_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_2Eoption_2Eoption(A_27a),V0opt_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))) = 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))))) # label(thm_2Eoption_2EOPTION__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1134 (all A_27a ((all V0x_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))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) # label(thm_2Eoption_2EIS__NONE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1135 (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]. 7.28/7.33 1136 (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]. 7.28/7.33 1137 (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]. 7.28/7.33 1138 (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]. 7.28/7.33 1139 (all A_27a ((all 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),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]. 7.28/7.33 1140 (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]. 7.28/7.33 1141 (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]. 7.28/7.33 1142 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.33 1143 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 ((s(tyop_2Eoption_2Eoption(A_27a),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_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V0x_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_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)))))) # label(thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1144 (all A_27a all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1145 (all A_27a all V0opt_2E0 ((exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0opt_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]. 7.28/7.34 1146 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),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)))) # label(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1147 (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 (s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0) & (all V6x_2E0 all V7y_2E0 (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),V3y2_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(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_27a),V1x2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0x1_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]. 7.28/7.34 1148 (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]. 7.28/7.34 1149 (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_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_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_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))))))) # label(thm_2Eoption_2EOPTION__MAP2__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1150 (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 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))))))) <-> (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))))))) # label(thm_2Eoption_2EFORALL__OPTION) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1151 (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__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))) = 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)))) # label(thm_2Eoption_2EOPTION__APPLY__MAP2) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1152 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2e_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 V6x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0)))) & (all V7x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0)))) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_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 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 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 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 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),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))))) & (all V17v_2E0 all V18f_2E0 s(A_27b,V17v_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)))) & (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_2ENONE_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))) & (all V22f_2E0 all 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))))) = 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)))))) & (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 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 V10x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) & (all V9x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V9x_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 V3x_2E0 all V4y_2E0 (s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4y_2E0))))))) # label(thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1153 (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)),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))) = 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)))) # 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]. 7.28/7.34 1154 (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_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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1155 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1156 (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]. 7.28/7.34 1157 (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]. 7.28/7.34 1158 (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),V2o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x1_2E0))) & s(A_27c,V0v_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(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V5x2_2E0))))))) # label(thm_2Eoption_2EOPTION__MAP2__SOME) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1159 (all A_27a all A_27b all V0y_2E0 all V1p_2E0 all V2f_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_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) | (exists V3x_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_27b),c_2Eoption_2ENONE_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_2ESOME_2E1(s(A_27b,V0y_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 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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0)))))))) # label(thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1160 (all A_27a all V0x_2E0 all V1X_2E0 all V2P_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_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))) = 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),V1X_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_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),V1X_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1X_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),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]. 7.28/7.34 1161 (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))) & (p(s(tyop_2Emin_2Ebool,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_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))))) # label(thm_2Eoption_2EOPTION__GUARD__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1162 (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]. 7.28/7.34 1163 (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]. 7.28/7.34 1164 (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]. 7.28/7.34 1165 (all A_27a all A_27b all V0v_2E0 all V1sc_2E0 all V2opt_2E0 all V3nc_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(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) & s(A_27b,V3nc_2E0) = s(A_27b,V0v_2E0) | (exists 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))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0),s(A_27a,V4x_2E0))) = s(A_27b,V0v_2E0))))) # label(thm_2Eoption_2Eoption__case__eq) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1166 (all A_27a all F0_2E0 all F1_2E0 ((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))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) -> ((all V0P_2E0 all V2x_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)),F1_2E0),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)))) -> (all V0P_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))))) # label(thm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1167 (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__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))) = 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)))) # label(thm_2Eoption_2EOPTION__MCOMP__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1168 (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]. 7.28/7.34 1169 (all A_27a all A_27b all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1170 (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),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))) # label(thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1171 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1172 (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]. 7.28/7.34 1173 (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]. 7.28/7.34 1174 (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]. 7.28/7.34 1175 (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]. 7.28/7.34 1176 (all A_27a all A_27b all A_27c all V0o2_2E0 all V1o1_2E0 all V2f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1o1_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_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))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__MAP2__NONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1177 (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]. 7.28/7.34 1178 (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]. 7.28/7.34 1179 (all A_27a all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__ALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1180 (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]. 7.28/7.34 1181 (all A_27a ((all V1P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,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)))))) & (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)))))) # label(thm_2Eoption_2EOPTION__ALL__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1182 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_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_2EIS__NONE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1183 (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)),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))) = 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)))) # 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]. 7.28/7.34 1184 (all A_27b all 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))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1185 (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]. 7.28/7.34 1186 (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]. 7.28/7.34 1187 (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]. 7.28/7.34 1188 (all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1189 (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),V3M_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(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,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(A_27a,V6x_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))) = 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))))) # label(thm_2Eoption_2Eoption__case__cong) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1190 (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_2ENONE_2E0)) # label(thm_2Eoption_2ENOT__NONE__SOME) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1191 (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]. 7.28/7.34 1192 (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,V2y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3z_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3z_2E0))))))) # label(thm_2Eoption_2EOPTION__MAP__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1193 (all A_27a all F1_2E0 all F0_2E0 ((all V0y_2E0 all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V0y_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)),F1_2E0),s(A_27a,V0y_2E0))),s(A_27a,V2x_2E0)))))) -> ((all V0y_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)),F0_2E0),s(A_27a,V0y_2E0))),s(A_27a,V1x_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0))) -> (all V0y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(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)),F0_2E0),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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V0y_2E0)))))))))) # label(thm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1194 (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]. 7.28/7.34 1195 (all A_27a ((all V1r_2E0 (s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),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))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & (all V0a_2E0 s(tyop_2Eoption_2Eoption(A_27a),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)))))))) # label(thm_2Eoption_2Eoption__REP__ABS__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1196 (all A_27a all A_27b all A_27c all F0_2E0 ((all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),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,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)),F0_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0)))))) -> (all V0f_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(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)),F0_2E0),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))) = 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)))))) # label(thm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1197 (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]. 7.28/7.34 1198 (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]. 7.28/7.34 1199 (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]. 7.28/7.34 1200 (all A_27a all A_27b all V0o1_2E0 all V1o2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(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),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),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]. 7.28/7.34 1201 (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]. 7.28/7.34 1202 (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]. 7.28/7.34 1203 (all A_27c all A_27d all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1204 (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]. 7.28/7.34 1205 (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]. 7.28/7.34 1206 (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)),c_2Eoption_2ESOME_2E1(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)),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)))) # 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]. 7.28/7.34 1207 (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)),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_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_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))) = 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]. 7.28/7.34 1208 (all 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))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__GUARD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1209 (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]. 7.28/7.34 1210 (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]. 7.28/7.34 1211 (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]. 7.28/7.34 1212 (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]. 7.28/7.34 1213 (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]. 7.28/7.34 1214 (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]. 7.28/7.34 1215 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),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)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1216 (all A_27a ((all V0x_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_2Ebool_2ET_2E0)) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) # label(thm_2Eoption_2EIS__SOME__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1217 (all A_27a all A_27b all V0y_2E0 all V1m2_2E0 all V2m1_2E0 (((exists 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_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),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_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))) = 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)))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1218 (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]. 7.28/7.34 1219 (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]. 7.28/7.34 1220 (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]. 7.28/7.34 1221 (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]. 7.28/7.34 1222 (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]. 7.28/7.34 1223 (all A_27a all V0y_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),c_2Eoption_2ESOME_2E1(s(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,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(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) & p(s(tyop_2Emin_2Ebool,V2P_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2P_2E0)) & s(A_27a,V1x_2E0) = 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_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_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)))))))) # label(thm_2Eoption_2EIF__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1224 (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__induction) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1225 (all A_27a all A_27b ((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)) & (all V0f_2E0 all 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))))) = 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)))))))) # label(thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1226 (all A_27a all A_27b all V0e_2E0 all V1f_2E0 exists V2fn_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))) = s(A_27b,V0e_2E0) & (all 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,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)))))))) # label(thm_2Eoption_2Eoption__Axiom) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1227 (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_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))) = 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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1228 (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]. 7.28/7.34 1229 (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),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0)))) # label(thm_2Eoption_2Eoption__case__ID) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1230 (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__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))) = 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)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MCOMP_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1231 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_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))) # label(thm_2Eoption_2EOPTION__MAP__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1232 (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]. 7.28/7.34 1233 (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]. 7.28/7.34 1234 (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]. 7.28/7.34 1235 (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_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))))) = 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)))) # label(thm_2Eoption_2EOPTION__MCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1236 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,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)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1237 (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]. 7.28/7.34 1238 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),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)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1239 (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]. 7.28/7.34 1240 (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]. 7.28/7.34 1241 (all A_27a all A_27b ((all V1x_2E0 all 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))) = 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)))) & (all V0f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_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)))))) # label(thm_2Eoption_2EOPTION__BIND__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1242 (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]. 7.28/7.34 1243 (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]. 7.28/7.34 1244 (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]. 7.28/7.34 1245 (all A_27a all A_27b all F0_2E0 ((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,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)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) -> (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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),F0_2E0),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]. 7.28/7.34 1246 (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__CASES) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1247 (all A_27a all F0_2E0 ((all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V0x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1248 (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]. 7.28/7.34 1249 (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]. 7.28/7.34 1250 (all A_27b 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_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),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)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1251 (all A_27a all A_27b all F0_2E0 ((all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (s(A_27a,V2a_2E0) = s(A_27a,V0x_2E0) & s(A_27b,V3b_2E0) = s(A_27b,V1y_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(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)))),F0_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))),s(A_27a,V2a_2E0))),s(A_27b,V3b_2E0)))))) -> (all V0x_2E0 all 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))) = 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)),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)))),F0_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))))))) # label(thm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1252 (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__VAR) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1253 (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_27a,V3a_2E0) = s(A_27a,V1x_2E0) & s(A_27b,V0y_2E0) = s(A_27b,V2b_2E0))) # label(thm_2Epair_2EPAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.34 1254 (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_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))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(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]. 7.28/7.34 1255 (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),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))) = 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)))) # 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]. 7.28/7.34 1256 (all A_27b all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(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]. 7.28/7.34 1257 (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]. 7.28/7.34 1258 (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]. 7.28/7.34 1259 (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]. 7.28/7.34 1260 (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]. 7.28/7.34 1261 (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]. 7.28/7.35 1262 (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]. 7.28/7.35 1263 (all A_27a all A_27b all X0_2E0 s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),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)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1264 (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]. 7.28/7.35 1265 (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]. 7.28/7.35 1266 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V2a_2E0) & s(A_27b,V1y_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(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0))))) # label(thm_2Epair_2ECLOSED__PAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1267 (all A_27b all A_27c all 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))) = s(A_27b,c_2Epair_2EFST_2E1(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]. 7.28/7.35 1268 (all A_27a all A_27b all A_27c all V0v_2E0 all V1p_2E0 all V2f_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))) = s(A_27a,V0v_2E0) <-> (exists V3x_2E0 exists V4y_2E0 (s(A_27a,V0v_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(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))))))) # label(thm_2Epair_2Epair__case__eq) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1269 (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]. 7.28/7.35 1270 (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]. 7.28/7.35 1271 (all A_27a all A_27b all V0p_2E0 all V1q_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0) = 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(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) # label(thm_2Epair_2EPAIR__FST__SND__EQ) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1272 (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_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))))) = 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)))))) # label(thm_2Epair_2EPAIR__MAP__THM) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1273 (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]. 7.28/7.35 1274 (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__thm) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1275 (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_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))) = 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)))) # 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]. 7.28/7.35 1276 (all A_27a all A_27b all F0_2E0 ((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)),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))),F0_2E0),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)))) -> (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)),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))),F0_2E0),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]. 7.28/7.35 1277 (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]. 7.28/7.35 1278 (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]. 7.28/7.35 1279 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1280 (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]. 7.28/7.35 1281 (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_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))) = 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)))))) # label(thm_2Epair_2EC__UNCURRY__L) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1282 (all A_27a all A_27b all A_27c all F0_2E0 ((all V0P_2E0 all V2p1_2E0 all V3p2_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))),F0_2E0),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)))))) -> (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)),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))),F0_2E0),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]. 7.28/7.35 1283 (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]. 7.28/7.35 1284 (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]. 7.28/7.35 1285 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all 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)))))) <-> 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)))))) # label(thm_2Epair_2EPROD__ALL__def) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1286 (all A_27a all A_27b all A_27c all A_27d all V0p_2E0 all V1f_2E0 all V2g_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))))) = 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)))))) # label(thm_2Epair_2EFST__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 7.28/7.35 1287 (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]. 7.28/7.35 1288 (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]. 7.28/7.35 1289 (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]. 7.28/7.35 1290 (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]. 7.28/7.35 1291 (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]. 7.38/7.35 1292 (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]. 7.38/7.35 1293 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1294 (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]. 7.38/7.35 1295 (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]. 7.38/7.35 1296 (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)),c_2Epair_2ECURRY_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))),c_2Epair_2ECURRY_2E0),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]. 7.38/7.35 1297 (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]. 7.38/7.35 1298 (all A_27a all A_27b all A_27c all V0g_2E0 all 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))) <-> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1f_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0g_2E0))) # label(thm_2Epair_2ECURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1299 (all A_27a all A_27b all V0x_2E0 all 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))))) = s(A_27b,V1y_2E0)) # label(thm_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1300 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1301 (all A_27b all A_27c all 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))) = s(A_27c,c_2Epair_2ESND_2E1(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]. 7.38/7.35 1302 (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]. 7.38/7.35 1303 (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]. 7.38/7.35 1304 (all A_27a all A_27b all F0_2E0 ((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)),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))),F0_2E0),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)))) -> (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)),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))),F0_2E0),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]. 7.38/7.35 1305 (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]. 7.38/7.35 1306 (all A_27a all A_27b all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Epair_2EPROD__ALL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1307 (all A_27a all A_27b all V0P_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))))))) <-> (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))))))) # label(thm_2Epair_2EELIM__PFORALL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1308 (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_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))))) = 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)))))) # label(thm_2Epair_2ES__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1309 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all 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))) = 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)))))) # label(thm_2Epair_2EUNCURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1310 (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]. 7.38/7.35 1311 (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]. 7.38/7.35 1312 (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]. 7.38/7.35 1313 (all A_27a all A_27b all V0y_2E0 all V1p_2E0 (s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V1p_2E0))) = s(A_27a,V0y_2E0) <-> (exists V2x_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(tyop_2Epair_2Eprod(A_27b,A_27a),V1p_2E0)))) # label(thm_2Epair_2ESND__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1314 (all A_27a all A_27b all A_27c all A_27d all F1_2E0 all F0_2E0 ((all V0P_2E0 all V2N_2E0 all V5x_2E0 all 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))))) = 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)))),F1_2E0),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)))) -> ((all V2N_2E0 all V3x_2E0 all 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)),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))),F0_2E0),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)))) -> (all V0P_2E0 all V1M_2E0 all V2N_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)),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))),F0_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,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)),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)))),F1_2E0),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))))))) # label(thm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1315 (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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_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(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_2Ereflexive__LEX) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1316 (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),V2P_2E0),s(A_27a,V6x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_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),V5Q_27_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,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))) = 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))))) # label(thm_2Epair_2EPROD__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1317 (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_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))))) = 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)))))) # label(thm_2Epair_2Eo__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1318 (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]. 7.38/7.35 1319 (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]. 7.38/7.35 1320 (all A_27a all A_27b all F0_2E0 ((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)),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))),F0_2E0),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)))) -> (all V0P_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)),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),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))))))))))) # label(thm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1321 (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]. 7.38/7.35 1322 (all A_27a all A_27b all F0_2E0 ((all V1p_2E0 (p(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),F0_2E0),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_27b,V5x_27_27_2E0) = s(A_27b,V3y_2E0) & s(A_27a,V2x_2E0) = s(A_27a,V4x_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)),V1p_2E0),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))))))) -> (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),F0_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]. 7.38/7.35 1323 (all A_27a all A_27b 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_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),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)))) # 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]. 7.38/7.35 1324 (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_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V1x_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,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]. 7.38/7.35 1325 (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]. 7.38/7.35 1326 (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]. 7.38/7.35 1327 (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]. 7.38/7.35 1328 (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))),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))) = 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)))) # 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]. 7.38/7.35 1329 (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]. 7.38/7.35 1330 (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]. 7.38/7.35 1331 (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]. 7.38/7.35 1332 (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]. 7.38/7.35 1333 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_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)))))) # label(thm_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1334 (all A_27a all A_27b all V0P_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))))) <-> (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))))))))) # label(thm_2Epair_2EELIM__PEXISTS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1335 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Epair_2EABS__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1336 (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]. 7.38/7.35 1337 (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]. 7.38/7.35 1338 (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)),V1f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0))) # label(thm_2Epair_2EUNCURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1339 (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]. 7.38/7.35 1340 (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]. 7.38/7.35 1341 (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]. 7.38/7.35 1342 (all A_27a1 all A_27a2 all A_27b all A_27c all F1_2E0 all F0_2E0 ((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,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)))),F1_2E0),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)))) -> ((all V1N_2E0 all V3x_2E0 all 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))) = 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)))),F0_2E0),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)))) -> (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)),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)))),F1_2E0),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))),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)))),F0_2E0),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]. 7.38/7.35 1343 (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]. 7.38/7.35 1344 (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]. 7.38/7.35 1345 (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)),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))) = 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)))) # 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]. 7.38/7.35 1346 (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_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_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_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]. 7.38/7.35 1347 (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]. 7.38/7.35 1348 (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_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))))))) = 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)))) # label(thm_2Epair_2EPAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1349 (all A_27a all A_27b all 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))) = s(A_27a,c_2Epair_2ESND_2E1(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]. 7.38/7.35 1350 (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]. 7.38/7.35 1351 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V0R1_2E0 all V2s_2E0 all V1R2_2E0 all V3t_2E0 all V4u_2E0 all 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)))) <-> 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(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)))))),F1_2E0),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)))))) -> ((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),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))))),F0_2E0),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)),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)))))),F1_2E0),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)))))) -> (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))),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))))),F0_2E0),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]. 7.38/7.35 1352 (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]. 7.38/7.35 1353 (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),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))) = 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)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1354 (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]. 7.38/7.35 1355 (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]. 7.38/7.35 1356 (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]. 7.38/7.35 1357 (all A_27a all A_27b all A_27d all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1358 (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]. 7.38/7.35 1359 (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]. 7.38/7.35 1360 (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]. 7.38/7.35 1361 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V0R1_2E0 all V2s_2E0 all V1R2_2E0 all V3t_2E0 all V4u_2E0 all 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_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)))))),F1_2E0),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_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)))) | s(A_27a,V4u_2E0) = s(A_27a,V2s_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)))))) -> ((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)),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)))))),F1_2E0),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),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))))),F0_2E0),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)))) -> (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))),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))))),F0_2E0),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]. 7.38/7.35 1362 (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]. 7.38/7.35 1363 (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]. 7.38/7.35 1364 (all A_27b all A_27d all X0_2E0 all 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))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(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]. 7.38/7.35 1365 (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]. 7.38/7.35 1366 (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) # label(axiom) # label(non_clause). [assumption]. 7.38/7.35 1367 (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),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))) = 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)))) # 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]. 7.38/7.35 1368 (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]. 7.38/7.35 1369 (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]. 7.38/7.36 1370 (all A_27a all A_27b all V0d_2E0 all V1c_2E0 all V2b_2E0 all V3a_2E0 all V4R2_2E0 all V5R1_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)))) & s(A_27a,V3a_2E0) = s(A_27a,V1c_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]. 7.38/7.36 1371 (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]. 7.38/7.36 1372 (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]. 7.38/7.36 1373 (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]. 7.38/7.36 1374 (all A_27a all A_27b ((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)))))) & (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))))))) # label(thm_2Epair_2EABS__REP__prod) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1375 (all A_27a all A_27b all V0P_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))))) <-> (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))))))))) # label(thm_2Epair_2EFORALL__PROD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1376 (all A_27a all A_27b all A_27c all F2_2E0 all F1_2E0 all F0_2E0 ((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),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))),F2_2E0),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)))) -> ((all V0P_2E0 all V2p_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)),F1_2E0),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)),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))),F2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0)))))) -> ((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),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)),F0_2E0),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,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)))) -> (all 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),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)),F1_2E0),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_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)),F0_2E0),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]. 7.38/7.36 1377 (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]. 7.38/7.36 1378 (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]. 7.38/7.36 1379 (all A_27a all A_27b all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1380 (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),V6v1_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v1_2E0) & (all V12a_2E0 all V13b_2E0 all V14c_2E0 all V15d_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(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) & s(A_27a,V12a_2E0) = s(A_27a,V14c_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,V12a_2E0),s(A_27b,V13b_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),V7v2_27_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),c_2Epair_2E_2C_2E2(s(A_27a,V8a_2E0),s(A_27b,V9b_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_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)),V0R1_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)),V4R1_27_2E0),s(A_27a,V8a_2E0))),s(A_27a,V10c_2E0))))) & s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v2_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_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]. 7.38/7.36 1381 (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]. 7.38/7.36 1382 (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]. 7.38/7.36 1383 (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]. 7.38/7.36 1384 (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]. 7.38/7.36 1385 (all A_27a all A_27b all 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))) = 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)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1386 (all A_27a all A_27b all V0x_2E0 all V1p_2E0 (s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))) = s(A_27a,V0x_2E0) <-> (exists V2y_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(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0)))) # label(thm_2Epair_2EFST__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1387 (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]. 7.38/7.36 1388 (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]. 7.38/7.36 1389 (all A_27a all A_27b all A_27c all V0f_27_2E0 all V1M_2E0 all V2M_27_2E0 all V3f_2E0 ((all V4x_2E0 all V5y_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(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_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(tyop_2Epair_2Eprod(A_27b,A_27c),V1M_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_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]. 7.38/7.36 1390 (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)),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)))))) # label(thm_2Epair_2ECURRY__UNCURRY__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1391 (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),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))) = 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)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1392 (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),V2M_27_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(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)),V1f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3M_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))))) # label(thm_2Epair_2EUNCURRY__CONG) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1393 (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]. 7.38/7.36 1394 (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]. 7.38/7.36 1395 (all A_27a all A_27b all 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))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ESWAP_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0)))) # label(thm_2Epair_2ESWAP__def) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1396 (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_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))) = 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)))) # 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]. 7.38/7.36 1397 (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]. 7.38/7.36 1398 (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))),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))) = 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)))) # 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]. 7.38/7.36 1399 (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]. 7.38/7.36 1400 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1401 (all A_27a all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1402 (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))),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))) = 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)))) # 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]. 7.38/7.36 1403 (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]. 7.38/7.36 1404 (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]. 7.38/7.36 1405 (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]. 7.38/7.36 1406 (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]. 7.38/7.36 1407 (all A_27a all A_27b all F0_2E0 ((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,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))),F0_2E0),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)))) -> (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))))) <-> 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)),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))))))) # label(thm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1408 (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]. 7.38/7.36 1409 (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]. 7.38/7.36 1410 (all A_27a all A_27b all A_27c all 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))) = 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)))) # 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]. 7.38/7.36 1411 (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]. 7.38/7.36 1412 (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]. 7.38/7.36 1413 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.38/7.36 1414 (all A_27a all F0_2E0 ((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,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(tyop_2Enum_2Enum,V2n_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(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)))),F0_2E0),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)))))) -> (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),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)))),F0_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__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1415 (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]. 7.38/7.36 1416 (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]. 7.38/7.36 1417 (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]. 7.38/7.36 1418 (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]. 7.38/7.36 1419 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,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)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1420 (all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1421 (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]. 7.38/7.36 1422 (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]. 7.38/7.36 1423 (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),V3g2_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,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)))) -> (all V6n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V4m1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V5m2_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]. 7.38/7.36 1424 (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]. 7.38/7.36 1425 (all A_27a all F1_2E0 all F0_2E0 ((all V0f_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)),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))),F1_2E0),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))) -> ((all V0f_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)),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))),F0_2E0),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))))) -> (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)),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))),F1_2E0),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)),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))),F0_2E0),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]. 7.38/7.36 1426 (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]. 7.38/7.36 1427 (all F0_2E0 ((all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V1y_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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1y_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)),F0_2E0))) = 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_2ELESS__ALT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1428 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = 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,V1n_2E0)))))) # label(thm_2Eprim__rec_2EEQ__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1429 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all 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))) = 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)))) # label(arityeq4_2Ec_2Eprim__rec_2EPRIM__REC__FUN_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1430 (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]. 7.38/7.36 1431 (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]. 7.38/7.36 1432 (all A_27a all V0P_2E0 all V1R_2E0 all 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)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2a_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]. 7.38/7.36 1433 (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]. 7.38/7.36 1434 (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]. 7.38/7.36 1435 (all F0_2E0 ((all V0x_2E0 all V1y_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)),F0_2E0),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))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0)))))) # label(thm_2Eprim__rec_2EWF__PRED) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1436 (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,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)))))))))) # label(thm_2Eprim__rec_2ELESS__SUC__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1437 (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]. 7.38/7.36 1438 (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]. 7.38/7.36 1439 (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]. 7.38/7.36 1440 (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,V1n_2E0) != 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,V1n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1441 (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]. 7.38/7.36 1442 (all A_27a all F0_2E0 ((all V0e_2E0 all V1f_2E0 all V2fn1_2E0 ((all 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),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_2E0_2E0))) = s(A_27a,V0e_2E0) <-> p(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))),F0_2E0),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 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),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))),F0_2E0),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]. 7.38/7.36 1443 (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]. 7.38/7.36 1444 (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]. 7.38/7.36 1445 (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__LEMMA1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1446 (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]. 7.38/7.36 1447 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1448 (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]. 7.38/7.36 1449 (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]. 7.38/7.36 1450 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Eprim__rec_2ESUC__ID) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1451 (all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1452 (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]. 7.38/7.36 1453 (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_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(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)))) # label(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1454 (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]. 7.38/7.36 1455 (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]. 7.38/7.36 1456 (all A_27a all 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))) = 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_2Eprim__rec_2EWF__IFF__WELLFOUNDED) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1457 (all A_27a all V0x_2E0 all V1f_27_2E0 all V2n_2E0 exists V3g_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)))))) & 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))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1458 (all A_27a all V0x_2E0 all 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,c_2Enum_2E0_2E0))) = s(A_27a,V0x_2E0) & (all 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))))) = 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)))))))) # label(thm_2Eprim__rec_2ESIMP__REC__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1459 (all F0_2E0 all F1_2E0 ((all V0m_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) -> ((all V0m_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)),F1_2E0),s(tyop_2Enum_2Enum,V0m_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,V1n_2E0))))) -> (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),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]. 7.38/7.36 1460 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Eprim__rec_2ESIMP__REC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1461 (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]. 7.38/7.36 1462 (all F1_2E0 all F0_2E0 ((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,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)),F1_2E0),s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,V5y_2E0)))))) -> ((all V2x_2E0 all V3y_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,V3y_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)),F0_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,V3y_2E0)))))) -> (all V0m_2E0 all 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)),F1_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,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)),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) # label(thm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1463 (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]. 7.38/7.36 1464 (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,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Eprim__rec_2ELESS__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1465 (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]. 7.38/7.36 1466 (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]. 7.38/7.36 1467 (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]. 7.38/7.36 1468 (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]. 7.38/7.36 1469 (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]. 7.38/7.36 1470 (all A_27a all F1_2E0 all F0_2E0 ((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,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))),F1_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),V3fun_2E0))),s(tyop_2Enum_2Enum,V4n_2E0)))) -> ((all V0x_2E0 all V2n_2E0 s(A_27a,V0x_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)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) -> (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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),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)),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))),F1_2E0),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]. 7.38/7.36 1471 (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]. 7.38/7.36 1472 (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]. 7.38/7.36 1473 (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]. 7.38/7.36 1474 (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]. 7.38/7.36 1475 (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]. 7.38/7.36 1476 (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]. 7.38/7.36 1477 (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]. 7.38/7.36 1478 (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]. 7.38/7.36 1479 (all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1480 (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(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(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,V1x_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))))) # label(thm_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1481 (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))),c_2Erelation_2Einv__image_2E1(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))),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)))) # label(arityeq1_2Ec_2Erelation_2Einv__image_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1482 (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]. 7.38/7.36 1483 (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]. 7.38/7.36 1484 (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]. 7.38/7.36 1485 (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]. 7.38/7.36 1486 (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]. 7.38/7.36 1487 (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]. 7.38/7.36 1488 (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]. 7.38/7.36 1489 (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]. 7.38/7.36 1490 (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]. 7.38/7.36 1491 (all V0m_2E0 all V1n_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,V0m_2E0))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Eprim__rec_2EINV__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.36 1492 (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]. 7.38/7.36 1493 (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]. 7.38/7.36 1494 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1495 (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]. 7.38/7.37 1496 (all A_27a all V0x_2E0 all V1f_2E0 ((all V2n_2E0 s(A_27a,V0x_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)))) & (all V3m_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,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))) = 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)))))) # label(thm_2Eprim__rec_2EPRIM__REC__EQN) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1497 (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]. 7.38/7.37 1498 (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_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1499 (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) -> 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]. 7.38/7.37 1500 (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]. 7.38/7.37 1501 (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,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__CASES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1502 (all V0P_2E0 ((all V1n_2E0 ((all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_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,V2m_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)))))) -> (all V3n_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_2ECOMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1503 (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_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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_2D_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,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1504 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = 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_2ETIMES2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1505 (all V0m_2E0 all V1n_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_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))))))) # label(thm_2Earithmetic_2EZERO__LESS__EXP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1506 (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_2D_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_2D_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__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1507 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2x_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_2EDIV__DIV__DIV__MULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1508 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1509 (all A_27a ((all V3R_2E0 all V4n_2E0 all V5x_2E0 all V6y_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,V4n_2E0))),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) <-> (exists 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)),V3R_2E0),s(A_27a,V5x_2E0))),s(A_27a,V7z_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,V4n_2E0),s(A_27a,V7z_2E0),s(A_27a,V6y_2E0)))))))) & (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_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))))) # label(thm_2Earithmetic_2ENRC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1510 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_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_2EEVEN__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1511 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))))) # label(thm_2Earithmetic_2EX__MOD__Y__EQ__X) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1512 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),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,c_2Earithmetic_2EEXP_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,V0m_2E0)))))) # label(thm_2Earithmetic_2EEXP2__LT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1513 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ELESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1514 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EFACT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EFACT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1515 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2ESUB__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1516 (all A_27a all V0z_2E0 all V1x_2E0 all V2n_2E0 all V3m_2E0 all V4R_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)),V4R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V5y_2E0),s(A_27a,V0z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Enum_2Enum,V3m_2E0),s(A_27a,V1x_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)),V4R_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0z_2E0)))))) # label(thm_2Earithmetic_2ENRC__ADD__EQN) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1517 (all V0n_2E0 all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V3z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V3z_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1518 (all V0m_2E0 all V1n_2E0 (s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) != s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_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_2EODD__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1519 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMIN__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1520 (all X0_2E0 all X1_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)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1521 (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 V1k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__MOD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1522 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1523 (all V0q_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))),s(tyop_2Enum_2Enum,V2m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EMOD__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1524 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ENOT__ODD__EQ__EVEN) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1525 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1526 (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]. 7.38/7.37 1527 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Earithmetic_2EMODEQ_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EMODEQ_2E3) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1528 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(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,V1m_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,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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,V1m_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,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))))) # label(thm_2Earithmetic_2EMODEQ__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1529 (all V0m_2E0 all 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))))) = 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_2EADD__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1530 (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_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEVEN_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1531 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_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,V0m_2E0))))) = 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__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1532 (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,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1533 (all A_27a all V0x_2E0 all V1f_2E0 all V2m_2E0 all V3n_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_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_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V0x_2E0)))) # label(thm_2Earithmetic_2EFUNPOW__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1534 (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_2ERTC_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_2ERTC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1535 (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)))) & 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_2Earithmetic_2ELESS__EQ__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1536 (all X0_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)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1537 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(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))))))) = s(tyop_2Enum_2Enum,V0n_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))))) # label(thm_2Earithmetic_2EEXP__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1538 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EABS__DIFF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EABS__DIFF_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1539 (all V0m_2E0 all 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))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2ESUC__ADD__SYM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1540 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_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,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))))) # label(thm_2Earithmetic_2EMIN__LE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1541 (all V0x_2E0 all V1y_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,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_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,V0x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) # label(thm_2Earithmetic_2EONE__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1542 (all V0x_2E0 all V1y_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))))) # label(thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1543 (all V0n_2E0 all V1a_2E0 all V2b_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_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ESUC__MOD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1544 (all A_27a all V0f_2E0 all V1g_2E0 ((all V4n_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)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))))) & (all V3n_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)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_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,V3n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))) <-> (all V2n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ESUC__ELIM__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1545 (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)))) -> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2ESUB__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1546 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))))))) # label(thm_2Earithmetic_2EBIT2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 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]. 7.38/7.37 1548 (all V0n_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> (all V2m_2E0 ((s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))) & (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))) # label(thm_2Earithmetic_2EPRE__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1549 (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_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(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]. 7.38/7.37 1550 (all V0z_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,V0z_2E0) <-> s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Earithmetic_2EMULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1551 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ESUB__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1552 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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_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_2ELESS__MONO__MULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1553 (all V0k_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (exists V2r_2E0 exists V3q_2E0 (s(tyop_2Enum_2Enum,V0k_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EDA) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1554 (all V0m_2E0 all V1n_2E0 all 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,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_2ELESS__MONO__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1555 (all V0m_2E0 all 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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1556 (all V0a_2E0 all V1m_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0a_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,V0a_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,V2n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2Efindq__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1557 (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_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EZERO__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1558 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_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)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ELT__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1559 (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)))) | (exists V2m_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,V2m_2E0))))))) <-> (exists 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))))))) # label(thm_2Earithmetic_2EEXISTS__NUM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1560 (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_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_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)))))) # label(thm_2Earithmetic_2EMOD__SUC__IFF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1561 (all V0p_2E0 all V1q_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,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V0p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1q_2E0))))))) # label(thm_2Earithmetic_2EEXP__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1562 (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]. 7.38/7.37 1563 (all X0_2E0 all X1_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)),app_2E2(s(tyop_2Emin_2Efun(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_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(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_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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0))),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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_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)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0),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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1564 (all V0m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2ELESS__EQ__REFL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1565 (all V0m_2E0 all V1n_2E0 all V2p_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)))) <-> 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)))))))) # label(thm_2Earithmetic_2ELE__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1566 (all V0n_2E0 all V1m1_2E0 all V2m2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m1_2E0),s(tyop_2Enum_2Enum,V2m2_2E0)))) <-> (exists V3a_2E0 exists V4b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V4b_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2m2_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m1_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__DEF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1567 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (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,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2p_2E0))) # label(thm_2Earithmetic_2EEQ__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1568 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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,V2z_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))))) # label(thm_2Earithmetic_2EX__LT__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1569 (all V0P_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)))) -> 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,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_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))))))) # label(thm_2Earithmetic_2EFORALL__NUM__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1570 (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_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Earithmetic_2ENRC__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1571 (all V0n_2E0 all V1m_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_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__ADD__SAME) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1572 (all V0n_2E0 all V1a_2E0 all V2b_2E0 all V3p_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,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2b_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,V1a_2E0),s(tyop_2Enum_2Enum,V3p_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,V2b_2E0),s(tyop_2Enum_2Enum,V3p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EADD__MOD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1573 (all V0n_2E0 all V1m_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_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_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))))) | s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EEXP__EQ__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1574 (all V0n1_2E0 all V1n2_2E0 all V2m1_2E0 all V3m2_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V1n2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V3m2_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V2m1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1n2_2E0),s(tyop_2Enum_2Enum,V3m2_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__SUMS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1575 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMULT__LESS__EQ__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1576 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_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)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1577 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> (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))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EADD__EQ__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1578 (all V0n_2E0 all V1e1_2E0 all V2e0_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,V2e0_2E0),s(tyop_2Enum_2Enum,V1e1_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1e1_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2e0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__INTRO__CONG) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1579 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (exists V2k_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2k_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQUAL__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1580 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V2p_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) | s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V2p_2E0))) # label(thm_2Earithmetic_2ESUB__RIGHT__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1581 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_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,V1y_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1y_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,V0x_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))))) # label(thm_2Earithmetic_2EONE__LT__MULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1582 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EGREATER__DEF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1583 (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]. 7.38/7.37 1584 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMOD__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1585 (all V0x_2E0 all V1y_2E0 all V2z_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1586 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EMULT__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1587 (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]. 7.38/7.37 1588 (all V0P_2E0 ((exists 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))))) -> (exists V2n_2E0 ((all V3m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_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,V3m_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_2Earithmetic_2EWOP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1589 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELT__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1590 (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]. 7.38/7.37 1591 (all V0n_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_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,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EDIV__LE__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1592 (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__COMM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1593 (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 V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EINV__PRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1594 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EINV__PRE__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1595 (all V0m_2E0 all V1n_2E0 all 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))))) = 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)))) # label(thm_2Earithmetic_2EMAX__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1596 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(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)))))) -> 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_2Earithmetic_2ELESS__MONO__ADD__INV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1597 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))))) # label(thm_2Earithmetic_2EMIN__LT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1598 (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]. 7.38/7.37 1599 (all V0n_2E0 all V1m_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)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(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,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_2Eprim__rec_2E_3C_2E2(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_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)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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))))))))) # label(thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1600 (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__ODD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1601 (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)))) <-> -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_2Earithmetic_2ENOT__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1602 (all X0_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)),app_2E2(s(tyop_2Emin_2Efun(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))),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))),c_2Epair_2EUNCURRY_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))),X0_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)),c_2Epair_2EUNCURRY_2E1(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))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1603 (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,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1604 (all A_27a all V0v_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4v_2E0 all V5f_2E0 ((s(tyop_2Enum_2Enum,V3M_27_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(A_27a,V0v_27_2E0) = s(A_27a,V4v_2E0)) & (all V6n_2E0 (s(tyop_2Enum_2Enum,V3M_27_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(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,V6n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))) & s(tyop_2Enum_2Enum,V3M_27_2E0) = s(tyop_2Enum_2Enum,V2M_2E0) -> s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V3M_27_2E0),s(A_27a,V0v_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_27_2E0))) = s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V2M_2E0),s(A_27a,V4v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0))))) # label(thm_2Earithmetic_2Enum__case__cong) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1605 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1606 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2ESUC__ONE__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1607 (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,V0n_2E0),s(tyop_2Enum_2Enum,V1m_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)))))) <-> 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))))))) # label(thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1608 (all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))) -> (all V1b_2E0 exists V2a_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2a_2E0)))))))) # label(thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1609 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1610 (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__OR__ODD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1611 (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_2Earithmetic_2ESUC__NOT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1612 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1613 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2EMAX__LE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1614 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_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,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__GREATER) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1615 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1616 (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]. 7.38/7.37 1617 (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]. 7.38/7.37 1618 (all V0p_2E0 all V1m_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0p_2E0))))) <-> s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V2n_2E0))) # label(thm_2Earithmetic_2EMULT__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1619 (all V0m_2E0 all V1n_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_2E_2B_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_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EZERO__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1620 (all A_27a all V0f_2E0 all V1n_2E0 all V2x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(A_27a,V2x_2E0))))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(A_27a,V2x_2E0)))) # label(thm_2Earithmetic_2EFUNPOW__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1621 (all V0n_2E0 all V1m2_2E0 all V2m1_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,V1m2_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m1_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,V2m1_2E0),s(tyop_2Enum_2Enum,V1m2_2E0))))))) # label(thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1622 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1623 (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)))) -> ((exists V3n_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)))) & 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,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)))))))))) <-> (exists 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))))))))) # label(thm_2Earithmetic_2EBOUNDED__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1624 (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,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1625 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2ENOT__EXP__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1626 (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_2ELT__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1627 (all V0x_2E0 all V1n_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))))))) # label(thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1628 (all A_27a ((all V2f_2E0 all V3n_2E0 all V4x_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V4x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_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,V4x_2E0)))))) & (all V0f_2E0 all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Earithmetic_2EFUNPOW) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1629 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> (all V2p_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))))))) # label(thm_2Earithmetic_2ELESS__IMP__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1630 (all V0q_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))),s(tyop_2Enum_2Enum,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0q_2E0))))) # label(thm_2Earithmetic_2EDIV__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1631 (all V0n_2E0 (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,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1632 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EPRE__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1633 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EMAX__LT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1634 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,V1m_2E0))) # label(thm_2Earithmetic_2ELESS__EQUAL__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1635 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_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_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ELESS__MULT2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1636 (all V0p_2E0 all V1q_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V0p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))))) # label(thm_2Earithmetic_2EEXP__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1637 (all V0n_2E0 all V1k_2E0 all V2q_2E0 ((exists V3r_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V3r_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> s(tyop_2Enum_2Enum,V2q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EDIV__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1638 (all V0m_2E0 all 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)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Earithmetic_2ENOT__NUM__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1639 (all V0n_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V2q_2E0 s(tyop_2Enum_2Enum,V2q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EDIV__MULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1640 (all V0z_2E0 all V1y_2E0 all V2x_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,V2x_2E0))))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) = s(tyop_2Enum_2Enum,V1y_2E0)) & (s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> 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,V2x_2E0))))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0)))))) # label(thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1641 (all V0x_2E0 all V1n_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EMOD__LIFT__PLUS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1642 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V2p_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__EQ__LESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1643 (all V0y1_2E0 all V1y0_2E0 all V2x1_2E0 all V3x0_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V2x1_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V1y0_2E0),s(tyop_2Enum_2Enum,V0y1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V1y0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2x1_2E0),s(tyop_2Enum_2Enum,V0y1_2E0))))))))) # label(thm_2Earithmetic_2EMODEQ__MULT__CONG) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1644 (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 exists V2m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))))))) # label(thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1645 (all V0b_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V2a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1c_2E0))),s(tyop_2Enum_2Enum,V0b_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1c_2E0)))))))) # label(thm_2Earithmetic_2ESUB__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1646 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = 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_2EADD__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1647 (all V0m_2E0 all 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)))) -> (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__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1648 (all V0n_2E0 all V1d_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_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,V1d_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1d_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EDIV__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1649 (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]. 7.38/7.37 1650 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1651 (all V0m_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)) # label(thm_2Earithmetic_2EMULT__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1652 (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_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EDIVMOD__ID) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1653 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_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__MAX__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1654 (all V0p_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))) -> (s(tyop_2Enum_2Enum,V2m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))) # label(thm_2Earithmetic_2ESUB__CANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1655 (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]. 7.38/7.37 1656 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2EMIN__IDEM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1657 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_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_2Earithmetic_2EMIN__MAX__LT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1658 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1659 (all V0n_2E0 all V1k_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,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> (exists V2d_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0))))) # label(thm_2Earithmetic_2EMOD__EQ__0__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 7.38/7.37 1660 (all V0n_2E0 all V1m_2E0 all V2b_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V2b_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_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,V2b_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,V2b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V2b_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LE__IFF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1661 (all V0P_2E0 all V1m_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),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (all V3q_2E0 all V4r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) = s(tyop_2Enum_2Enum,V1m_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3q_2E0))))))))) # label(thm_2Earithmetic_2EDIV__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1662 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__CASES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1663 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Enum_2Enum,V1m_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))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),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,V1m_2E0)))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1664 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1665 (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]. 7.38/7.38 1666 (all V0m_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)))) # label(thm_2Earithmetic_2EMULT__LEFT__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1667 (all V0z_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0z_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,V0z_2E0)))) # label(thm_2Earithmetic_2EEXP__BASE__MULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1668 (all V0n_2E0 all V1q_2E0 all V2r_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_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMOD__TIMES__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1669 (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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1670 (all V0n_2E0 all V1k_2E0 all V2r_2E0 ((exists V3q_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V2r_2E0))) # label(thm_2Earithmetic_2EMOD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1671 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(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_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EADD1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1672 (all V0a_2E0 all V1c_2E0 s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1c_2E0))),s(tyop_2Enum_2Enum,V1c_2E0)))) # label(thm_2Earithmetic_2EADD__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1673 (all V0n_2E0 all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) # label(thm_2Earithmetic_2EMODEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1674 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_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__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1675 (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)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0)))))) # label(thm_2Earithmetic_2EMOD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1676 (all V0x_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))) <-> s(tyop_2Enum_2Enum,V0x_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_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Earithmetic_2EX__LT__EXP__X__IFF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1677 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1678 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) # label(thm_2Earithmetic_2ESUB__RIGHT__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1679 (all A_27a all V0f_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_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))))))) # label(thm_2Earithmetic_2Etransitive__measure) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1680 (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]. 7.38/7.38 1681 (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]. 7.38/7.38 1682 (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 V1k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V1k_2E0))))) # label(thm_2Earithmetic_2EDIVISION) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1683 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1684 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_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,V0m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(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,V1n_2E0)))))))) # label(thm_2Earithmetic_2EMULT__INCREASES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1685 (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 V2b_2E0 exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2b_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__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1686 (all V0m_2E0 all V1n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_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_2ENOT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1687 (all V0y_2E0 all V1x_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_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))) & 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_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_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))))) # label(thm_2Earithmetic_2EMOD__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1688 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),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_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1689 (all V0x_2E0 all V1z_2E0 all V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V1z_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1z_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__PLUS__LE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1690 (all V0n_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) -> (exists V1m_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = 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,V1m_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) -> (exists V2m_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = 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,V2m_2E0))))))))) # label(thm_2Earithmetic_2EEVEN__ODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1691 (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]. 7.38/7.38 1692 (all V0m_2E0 all V1n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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_2ENOT__LESS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1693 (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_2A_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_2A_2E2(s(tyop_2Enum_2Enum,V0m_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_2EMULT__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1694 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (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,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__EXP__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1695 (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 V1k_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1k_2E0))))))) # label(thm_2Earithmetic_2EDIV__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1696 (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_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_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,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_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,V0m_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EMULT__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1697 (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)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ESUB__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1698 (all F6_2E0 all F0_2E0 all F4_2E0 all F5_2E0 all F3_2E0 all F2_2E0 all F1_2E0 ((all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_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)),F6_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) -> ((all V0a_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)),F6_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> ((all V6n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V6n_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Enum_2Enum,V6n_2E0)))))) -> ((all V5m_2E0 all V4a_2E0 all V3f_2E0 all V7d_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V7d_2E0))),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Enum_2Enum,app_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_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,V4a_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V7d_2E0))))))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),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_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F5_2E0),s(tyop_2Enum_2Enum,V5m_2E0))),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_2Enum_2Enum,V7d_2E0)))) -> ((all V4a_2E0 all V3f_2E0 all V5m_2E0 all V6n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),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_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F5_2E0),s(tyop_2Enum_2Enum,V5m_2E0))),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_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,V6n_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_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),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_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,V6n_2E0)))) -> ((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)),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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),F2_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_2Enum_2Enum,V4a_2E0)))) -> ((all V3f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),F2_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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),F1_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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),F0_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),F1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Earithmetic_2Efindq_2E0))))))))) # label(thm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1699 (all V0m_2E0 all V1n_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2k_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2k_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EDIV__MOD__MOD__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1700 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = 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,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_2EEQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1701 (all V0n_2E0 all V1m_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ENOT__SUC__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1702 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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) | 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_2Earithmetic_2ELESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1703 (all V0m_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(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)))))))) # label(thm_2Earithmetic_2ESUC__SUB1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1704 (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,V2n_2E0),s(A_27a,V5y_2E0),s(A_27a,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,V1m_2E0),s(A_27a,V3x_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Earithmetic_2ENRC__ADD__E) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1705 (all V0n_2E0 all V1m_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1706 (all V0n_2E0 all V1m_2E0 all V2i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ELESS__SUB__ADD__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1707 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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_2Earithmetic_2EMIN__DEF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1708 (all V0m_2E0 all 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)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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)))))))))))) # label(thm_2Earithmetic_2ESUB__LESS__OR) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1709 (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]. 7.38/7.38 1710 (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,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))))) = 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)))) # label(thm_2Earithmetic_2ERIGHT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1711 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Earithmetic_2EEQ__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1712 (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_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EEXP__BASE__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1713 (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,V1x_2E0),s(tyop_2Enum_2Enum,V0n_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__LEFT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1714 (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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2ENRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1715 (all V0P_2E0 all V1m_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)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1m_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_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_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_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2EMIN__MAX__PRED) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1716 (all V0m_2E0 all 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)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_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,V0m_2E0)))) # label(thm_2Earithmetic_2ELESS__ADD__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1717 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) # label(thm_2Earithmetic_2EMIN__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1718 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EABS__DIFF__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1719 (all V0m_2E0 all V1n_2E0 (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,V1n_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,V1n_2E0))))) # label(thm_2Earithmetic_2EMULT__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1720 (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 V3n_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,V3n_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))))))) # label(thm_2Earithmetic_2ERTC__NRC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1721 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,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_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2EEVEN__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1722 (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]. 7.38/7.38 1723 (all A_27a all V0R_2E0 all V1n_2E0 all V2x_2E0 all V3y_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,V1n_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,V3y_2E0)))))) # label(thm_2Earithmetic_2ENRC__RTC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1724 (all V0P_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))))) <-> (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,c_2Enum_2ESUC_2E1(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_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2EFORALL__NUM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1725 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_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_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) # label(thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1726 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))))) # label(thm_2Earithmetic_2EX__LE__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1727 (all F0_2E0 all F1_2E0 ((all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> ((all V2a_2E0 all V1m_2E0 all V0n_2E0 all V3q_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3q_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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,V3q_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),F1_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V3q_2E0)))) -> (all V0n_2E0 all V1m_2E0 all V2a_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_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,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1m_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),F1_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_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,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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,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,V0n_2E0))))))))))) # label(thm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1728 (all V0m_2E0 all V1n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_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,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ENOT__GREATER) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1729 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) <-> (exists V1m_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = 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,V1m_2E0)))))) # label(thm_2Earithmetic_2EEVEN__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1730 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EODD__EXP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1731 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_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,V1x_2E0),s(A_27a,V0y_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)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0y_2E0)))) # label(thm_2Earithmetic_2ENRC__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1732 (all V0p_2E0 all V1q_2E0 all V2n_2E0 all V3m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1q_2E0))),s(tyop_2Enum_2Enum,V0p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1q_2E0))),s(tyop_2Enum_2Enum,V0p_2E0))))) <-> s(tyop_2Enum_2Enum,V3m_2E0) = s(tyop_2Enum_2Enum,V2n_2E0))) # label(thm_2Earithmetic_2EMULT__EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1733 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_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_2EEXP__EXP__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1734 (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,V1x_2E0)))) | s(tyop_2Enum_2Enum,V0y_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,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))))) # label(thm_2Earithmetic_2EZERO__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1735 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_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,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ESUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1736 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2ESUB_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1737 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EZERO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1738 (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_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__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1739 (all V0m_2E0 all 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)))) | 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_2Earithmetic_2ELESS__LESS__CASES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1740 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) | 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,V2p_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2ESUB__LEFT__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1741 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_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_2ESUB__RIGHT__GREATER) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1742 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) | (exists V1n_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2Enum__CASES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1743 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2EMAX__IDEM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1744 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) <-> (exists V1m_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = 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,V1m_2E0)))))))) # label(thm_2Earithmetic_2EODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1745 (all V0p_2E0 all V1m_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0p_2E0))))))) # label(thm_2Earithmetic_2ESUB__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1746 (all V0m_2E0 all V1n_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_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_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,V0m_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V1n_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))))))) # label(thm_2Earithmetic_2EADD__EQ__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1747 (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]. 7.38/7.38 1748 (all F0_2E0 all F1_2E0 ((all V0n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) -> ((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,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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V3d_2E0)))) -> (all V0n_2E0 all V1m_2E0 all 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,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,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))),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_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1749 (all V0n_2E0 all V1q_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,V1q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMULT__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1750 (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_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1751 (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_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1752 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_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)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_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)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1753 (all V0b_2E0 all V1a_2E0 all V2P_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_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))))) <-> (all V3d_2E0 ((s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V3d_2E0))) = s(tyop_2Enum_2Enum,V1a_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V3d_2E0))))) & (s(tyop_2Enum_2Enum,V0b_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V3d_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_2E0_2E0))))))))) # label(thm_2Earithmetic_2ESUB__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1754 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(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,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMIN__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1755 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ELESS__ADD__NONZERO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1756 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1757 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) # label(thm_2Earithmetic_2EADD__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1758 (all V0m_2E0 all V1n_2E0 all V2p_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))))) = 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)))))) # label(thm_2Earithmetic_2ELEFT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1759 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EPRE__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1760 (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 V1k_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1761 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))) = s(tyop_2Enum_2Enum,V0m_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ESUC__PRE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1762 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,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)))))) # label(thm_2Earithmetic_2ELT__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1763 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3n_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,V3n_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_2Earithmetic_2ERTC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1764 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V1n_2E0))))))) # label(thm_2Earithmetic_2ELESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1765 (all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))) -> (all V1b_2E0 exists V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Earithmetic_2EONE__ONE__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1766 (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]. 7.38/7.38 1767 (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]. 7.38/7.38 1768 (all V0y_2E0 all V1x_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) # label(thm_2Earithmetic_2EMODEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1769 (all V0z_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_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,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V0z_2E0)))))))) # label(thm_2Earithmetic_2ELE__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1770 (all V0k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0k_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)) # label(thm_2Earithmetic_2EMOD__1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1771 (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_2B_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_2B_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__PLUS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1772 (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]. 7.38/7.38 1773 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EX__LE__X__EXP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1774 (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 V1m_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2EADD__DIV__RWT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1775 (all V0m_2E0 (s(tyop_2Enum_2Enum,V0m_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,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__0__CASES) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1776 (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]. 7.38/7.38 1777 (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]. 7.38/7.38 1778 (all V0p_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))) -> (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2m_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))))) # label(thm_2Earithmetic_2ECANCEL__SUB) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1779 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EGREATER__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1780 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1781 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),c_2Earithmetic_2Enum__CASE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2Enum__CASE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1782 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1783 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_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_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EZERO__LESS__MULT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1784 (all V0m_2E0 all 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)))) -> 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_2Earithmetic_2EOR__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1785 (all V0z_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V0z_2E0)))))))) # label(thm_2Earithmetic_2ELT__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1786 (all V0p_2E0 all V1q_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,V0p_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_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,V1q_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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,V0p_2E0))),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,V1q_2E0)))))) # label(thm_2Earithmetic_2EDOUBLE__LT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1787 (all V0k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0k_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2EMOD__ONE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1788 (all V0m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))) # label(thm_2Earithmetic_2ELESS__EQ__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1789 (all A_27a ((all V2n_2E0 all V3v_2E0 all V4f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V3v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0)))) & (all V0v_2E0 all V1f_2E0 s(A_27a,V0v_2E0) = s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0)))))) # label(thm_2Earithmetic_2Enum__case__def) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1790 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELE__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1791 (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 V1x_2E0 all V2r_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EADD__DIV__ADD__DIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1792 (all V0m_2E0 all V1i_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V1i_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))))) # label(thm_2Earithmetic_2EMULT__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1793 (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]. 7.38/7.38 1794 (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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1795 (all V0P_2E0 all V1x_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),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) & (all V3y_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_2B_2E2(s(tyop_2Enum_2Enum,V3y_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,V3y_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_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2EMOD__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1796 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EDIV2__def) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1797 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EPRE__SUB1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1798 (all 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_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Earithmetic_2EEXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1799 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Earithmetic_2EEXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1800 (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)))) <-> (exists V3n_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_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))))))) # label(thm_2Earithmetic_2ETC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1801 (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]. 7.38/7.38 1802 (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,V2m_2E0),s(tyop_2Enum_2Enum,V1n_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)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1803 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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_2Earithmetic_2EMAX__DEF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1804 (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]. 7.38/7.38 1805 (all V0n_2E0 all V1m_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2ELESS__EXP__SUC__MONO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.38 1806 (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]. 7.38/7.39 1807 (all V0n_2E0 all V1m2_2E0 all V2m1_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m2_2E0),s(tyop_2Enum_2Enum,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,V2m1_2E0) = s(tyop_2Enum_2Enum,V1m2_2E0) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V1m2_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1808 (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]. 7.38/7.39 1809 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMAX_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1810 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Earithmetic_2EADD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1811 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Earithmetic_2EADD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1812 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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_2ELESS__EQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1813 (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]. 7.38/7.39 1814 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> (all V2c_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V2c_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__SUB__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1815 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),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,c_2Earithmetic_2E_2B_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,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__LESS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1816 (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]. 7.38/7.39 1817 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2EADD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1818 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2p_2E0))) # label(thm_2Earithmetic_2EEQ__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1819 (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]. 7.38/7.39 1820 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2ELESS__DIV__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1821 (all V0n_2E0 all V1m_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,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2ESUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1822 (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,c_2Enum_2ESUC_2E1(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,V1n_2E0)))))))) # label(thm_2Earithmetic_2ENOT__STRICTLY__DECREASING) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1823 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2x_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,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMOD__MULT__MOD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1824 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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)))))) # label(thm_2Earithmetic_2ESUB__LEFT__ADD) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1825 (all V0m_2E0 all V1n_2E0 all V2i_2E0 all V3j_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V3j_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2i_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V3j_2E0)))))))) # label(thm_2Earithmetic_2ELESS__MONO__MULT2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1826 (all V0P_2E0 all V1m_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)))) -> ((all V3q_2E0 all V4r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4r_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_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Earithmetic_2EMOD__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1827 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Earithmetic_2Efindq_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_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)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2Efindq_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1828 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1829 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EPRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1830 (all V0P_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)))) -> ((exists V3k_2E0 exists V4r_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3k_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Enum_2Enum,V2q_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) = s(tyop_2Enum_2Enum,V1p_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_2EDIV_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))))))) # label(thm_2Earithmetic_2EDIV__P) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1831 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> 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,V0m_2E0))) # label(thm_2Earithmetic_2EADD__INV__0__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1832 (all V0y1_2E0 all V1y0_2E0 all V2x1_2E0 all V3x0_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V2x1_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V1y0_2E0),s(tyop_2Enum_2Enum,V0y1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V1y0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2x1_2E0),s(tyop_2Enum_2Enum,V0y1_2E0))))))))) # label(thm_2Earithmetic_2EMODEQ__PLUS__CONG) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1833 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Earithmetic_2ENUMERAL__DEF) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1834 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = 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,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_2EEQ__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1835 (all V0m_2E0 all 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,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ENOT__LEQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1836 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)) # label(thm_2Earithmetic_2EADD__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1837 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2EABS__DIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1838 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2p_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) # label(thm_2Earithmetic_2EEQ__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1839 (all V0b1_2E0 all V1b2_2E0 all V2x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b1_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b2_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) <-> s(tyop_2Enum_2Enum,V2x_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V0b1_2E0) = s(tyop_2Enum_2Enum,V1b2_2E0))) # label(thm_2Earithmetic_2EEXP__EXP__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1840 (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]. 7.38/7.39 1841 (all A_27a all V0R_2E0 all V1m_2E0 all V2n_2E0 all V3x_2E0 all V4y_2E0 all V5z_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,V4y_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,V4y_2E0),s(A_27a,V5z_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,V5z_2E0)))))) # label(thm_2Earithmetic_2ENRC__ADD__I) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1842 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = 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,V1m_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1843 (all V0P_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))))) <-> (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)))))))))))))) # label(thm_2Earithmetic_2ESUC__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1844 (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,V1x_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))))) # label(thm_2Earithmetic_2EADD__MODULUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1845 (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]. 7.38/7.39 1846 (all V0x_2E0 all V1z_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1z_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1z_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__SUC__LE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1847 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EFACT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1848 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V1m_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,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EMAX__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1849 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),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,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_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)))))))) # label(thm_2Earithmetic_2EMOD__2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1850 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2ESUB__LESS__0) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1851 (all V0x_2E0 all V1b_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,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))))) # label(thm_2Earithmetic_2EX__LT__EXP__X) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1852 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V1y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V2z_2E0)))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Earithmetic_2EDIV__EQ__X) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1853 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_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_2ESUB__RIGHT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1854 (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]. 7.38/7.39 1855 (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]. 7.38/7.39 1856 (all V0y_2E0 all V1x_2E0 all V2n_2E0 all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V3e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V3e_2E0)))))))) # label(thm_2Earithmetic_2EMODEQ__EXP__CONG) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1857 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2EGREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1858 (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]. 7.38/7.39 1859 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EMIN__COMM) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1860 (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_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_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2m_2E0))))) # label(thm_2Earithmetic_2EEXP__BASE__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1861 (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_2A_2E2(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,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2ELE__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1862 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EEVEN__EXP) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1863 (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_2A_2E2(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,V2p_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2ELE__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1864 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> (exists V2p_2E0 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,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1865 (all V0P_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)))) -> ((exists V3k_2E0 exists V4r_2E0 (s(tyop_2Enum_2Enum,V1p_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Enum_2Enum,V2q_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4r_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_2EMOD_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))))))) # label(thm_2Earithmetic_2EMOD__P) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1866 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_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,V0n_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) & (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(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_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))))))) # label(thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1867 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1868 (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]. 7.38/7.39 1869 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.38/7.39 1870 (all V0m_2E0 all V1n_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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,V2a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))))) # label(thm_2Earithmetic_2EDIVMOD__CORRECT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1871 (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)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2ESUB__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1872 (all V0n_2E0 exists V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))) | s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,V1m_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,V0n_2E0))) # label(thm_2Earithmetic_2EODD__OR__EVEN) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1873 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1874 (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__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1875 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1876 (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]. 7.43/7.39 1877 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),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,V1n_2E0)))) # label(thm_2Earithmetic_2EADD__COMM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1878 (all V0m_2E0 all 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)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__STRONG__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1879 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (exists V2p_2E0 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,V1n_2E0)))) # label(thm_2Earithmetic_2ELESS__EQUAL__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1880 (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))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))))) # label(thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1881 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1882 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EODD__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1883 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_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_2EINV__PRE__LESS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1884 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EDIVMOD__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1885 (all V2m_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2Enum_2E0_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))))))))))) # label(thm_2Earithmetic_2EDIVMOD__CALC_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1886 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),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,V1n_2E0)))) # label(thm_2Earithmetic_2EADD__SYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1887 (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]. 7.43/7.39 1888 (all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V2c_2E0)))) # label(thm_2Earithmetic_2ESUB__PLUS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1889 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2EABS__DIFF__EQS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1890 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = 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,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1891 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))))) # label(thm_2Earithmetic_2EBIT1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1892 (all V0a_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_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Earithmetic_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1893 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2ESUB__EQ__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1894 (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]. 7.43/7.39 1895 (all V0m_2E0 all V1i_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1i_2E0)))) # label(thm_2Earithmetic_2ELESS__MULT__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1896 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_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__SYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1897 (all A_27a all V0y_2E0 all V1x_2E0 all V2n_2E0 all V3R_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)))))) <-> 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)))))) # label(thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1898 (all V0z_2E0 all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0z_2E0))))))) # label(thm_2Earithmetic_2EABS__DIFF__LE__SUM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1899 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2Enat__elim____magic_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2Enat__elim____magic_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1900 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1901 (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,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Earithmetic_2EADD__INV__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1902 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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,V2z_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V0x_2E0))))) # label(thm_2Earithmetic_2EDIV__LE__X) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1903 (all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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)))))))))) # label(thm_2Earithmetic_2ELE__LT1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1904 (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_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1905 (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_2Earithmetic_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1906 (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,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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__NOT__SUC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1907 (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]. 7.43/7.39 1908 (all V0m_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1p_2E0)))) -> (all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ESUB__LESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1909 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1910 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2EMULT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1911 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Earithmetic_2EMULT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1912 (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]. 7.43/7.39 1913 (all A_27a all V0zc_2E0 all V1v_2E0 all V2sc_2E0 all V3n_2E0 ((exists V4x_2E0 (s(tyop_2Enum_2Enum,V3n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4x_2E0))) & s(A_27a,V1v_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2sc_2E0),s(tyop_2Enum_2Enum,V4x_2E0))))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V3n_2E0) & s(A_27a,V0zc_2E0) = s(A_27a,V1v_2E0) <-> s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V0zc_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2sc_2E0))) = s(A_27a,V1v_2E0))) # label(thm_2Earithmetic_2Enum__case__eq) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1914 (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,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,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))))))) # label(thm_2Earithmetic_2EMULT__EQ__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1915 (all A_27a all V0num_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),A_27a)),V0num_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))))))) # label(thm_2Earithmetic_2Edatatype__num) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1916 (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]. 7.43/7.39 1917 (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,V1x_2E0),s(tyop_2Enum_2Enum,V0n_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_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1918 (all V2n_2E0 all V3x_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)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Earithmetic_2EADD__MODULUS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1919 (all F3_2E0 all F4_2E0 all F2_2E0 all F1_2E0 all F0_2E0 ((all V3n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V3n_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) -> ((all V0f_2E0 all V1a_2E0 all V2m_2E0 all V3n_2E0 all V4q_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(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_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_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V4q_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V4q_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),F4_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,V1a_2E0))),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4q_2E0)))) -> ((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,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_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,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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),F4_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,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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),F2_2E0),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)))) -> ((all V0f_2E0 all V1a_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),F2_2E0),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_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_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)))),F1_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,V1a_2E0)))) -> ((all V0f_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)),c_2Epair_2EUNCURRY_2E1(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)))),F1_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_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)),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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_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_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)),c_2Earithmetic_2EDIVMOD_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)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_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)),c_2Epair_2ESND_2E0))))),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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0))))))))) # label(thm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1920 (all V0m_2E0 all V1n_2E0 all 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_2Earithmetic_2E_3C_3D_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,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__LESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1921 (all A_27a all V0x_2E0 all V1f_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Earithmetic_2EFUNPOW__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1922 (all V0x_2E0 all V1n_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2e_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2e_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EEXP__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1923 (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,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,V2q_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]. 7.43/7.39 1924 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EEVEN__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1925 (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]. 7.43/7.39 1926 (all V0n_2E0 all V1k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0))) # label(thm_2Earithmetic_2ELESS__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1927 (all X0_2E0 s(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1928 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V0x_2E0))))) # label(thm_2Earithmetic_2EDIV__LT__X) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1929 (all V0m_2E0 all V1n_2E0 (s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_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_2EEVEN__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1930 (all V0m_2E0 all V1n_2E0 all V2p_2E0 all V3q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V3q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V3q_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1931 (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]. 7.43/7.39 1932 (all V0m2_2E0 all V1m1_2E0 (s(tyop_2Enum_2Enum,V1m1_2E0) = s(tyop_2Enum_2Enum,V0m2_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m1_2E0),s(tyop_2Enum_2Enum,V0m2_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__0__CONG) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1933 (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]. 7.43/7.39 1934 (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) -> 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__CASES__IMP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1935 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELEFT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1936 (all V0n_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V2q_2E0 s(tyop_2Enum_2Enum,V1r_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1937 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(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)),c_2Earithmetic_2EDIVMOD_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIVMOD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1938 (all V0n_2E0 all V1m_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(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,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,V0n_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Earithmetic_2Efindq__divisor) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1939 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2EMIN__MAX__LE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1940 (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_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EZERO__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1941 (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,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))) = 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)))))) # label(thm_2Earithmetic_2EMOD__TIMES2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1942 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> 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]. 7.43/7.39 1943 (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 V1q_2E0 all V2r_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2r_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__TIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1944 (all V0n_2E0 all V1m_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1945 (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_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Earithmetic_2ESUB__LEFT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1946 (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_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1947 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMAX__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1948 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) | (exists V2p_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2ELESS__OR__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1949 (all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Earithmetic_2EEVEN__MOD2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.39 1950 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))),s(tyop_2Enum_2Enum,V1n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))))) # label(thm_2Earithmetic_2EEXP__SUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1951 (all 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,V0m_2E0)) # label(thm_2Earithmetic_2EMULT__RIGHT__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1952 (all V0n_2E0 all V1m_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,V1m_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EEXP__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1953 (all F0_2E0 ((all V0x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) <-> s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) -> (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_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,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Earithmetic_2EZERO__EXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1954 (all V0n_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)))) -> 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))))))) # label(thm_2Earithmetic_2EONE__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1955 (all V0p_2E0 all V1q_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,V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1q_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,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))))))) # label(thm_2Earithmetic_2EONE__LT__MULT__IMP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1956 (all V0z_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0z_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,V0z_2E0)))) # label(thm_2Earithmetic_2EEXP__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1957 (all A_27a 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)))) & (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,V2n_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))))))))) -> (all V3m_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V4n_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,V3m_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))))))) # label(thm_2Earithmetic_2Etransitive__monotone) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1958 (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,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))))) = 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_2ELT__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1959 (all V0q_2E0 s(tyop_2Enum_2Enum,V0q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0q_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)))))))) # label(thm_2Earithmetic_2EDIV__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1960 (all F0_2E0 ((all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V1y_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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1y_2E0)))))) -> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0))))) # label(thm_2Earithmetic_2ELESS__OR__EQ__ALT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1961 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Earithmetic_2EADD__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1962 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1963 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EMAX__COMM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1964 (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 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)))))) & 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 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))))))))) # label(thm_2Earithmetic_2EBOUNDED__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1965 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) != 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,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)))))) # label(thm_2Earithmetic_2ELESS__SUC__EQ__COR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1966 (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]. 7.43/7.40 1967 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_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,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1968 (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_2EODD__EVEN) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1969 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))) | s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EODD__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1970 (all A_27a all V0x_2E0 all V1f_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))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0x_2E0)))) # label(thm_2Earithmetic_2EFUNPOW__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1971 (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]. 7.43/7.40 1972 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1973 (all A_27a all F0_2E0 ((all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> (all V0g_2E0 all V1f_2E0 all V2n_2E0 s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0g_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0g_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Earithmetic_2Enum__case__compute) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1974 (all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) | s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ELE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1975 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2ELE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1976 (all V0y_2E0 all V1x_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0y_2E0)))))))) # label(thm_2Earithmetic_2EMODEQ__SUC__CONG) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1977 (all V0P_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) & (exists V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))) <-> (exists V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) & (all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V5y_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V5y_2E0)))))))))) # label(thm_2Earithmetic_2EEXISTS__GREATEST) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1978 (all V0q_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0q_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Enum_2Enum,V0q_2E0)) # label(thm_2Earithmetic_2EDIV__ONE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1979 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2Enat__elim____magic) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1980 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_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__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1981 (all V0c_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0c_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> (all V2a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0c_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__ADD__SUB) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1982 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Eposet_2Ecomplete_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eposet_2Ecomplete_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1983 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0)))) <-> (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,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,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4y_2E0)))))))))) # label(thm_2Eposet_2Emonotonic__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1984 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Edown__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eup__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Econtinuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))))) # label(thm_2Eposet_2Econtinuous__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1985 (all A_27a all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V2p_2E0),s(A_27a,V3x_2E0)))) <-> (all V5z_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)),V1r_2E0),s(A_27a,V5z_2E0))),s(A_27a,V6y_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)),V1r_2E0),s(A_27a,V5z_2E0))),s(A_27a,V3x_2E0)))))) & (all V4y_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),V0s_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)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Eglb__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1986 (all A_27a all V0s_2E0 all V1r_2E0 all V2c_2E0 ((all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_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)))) | 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,V4y_2E0))),s(A_27a,V3x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V2c_2E0)))))) # label(thm_2Eposet_2Echain__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1987 (all A_27a all F0_2E0 ((all V0s_2E0 all V2p_2E0 all V4j_2E0 (p(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(A_27a,V4j_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4j_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4j_2E0)))))) -> (all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V2p_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Eglb__pred) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1988 (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]. 7.43/7.40 1989 (all A_27a all V0p_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Ecomplete__up) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1990 (all A_27a all A_27b all F0_2E0 ((all V0t_2E0 all V2r_2E0 all V3f_2E0 all V4g_2E0 (p(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,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,A_27b),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_2Ebool),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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0)))) <-> (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_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_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V5x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0),s(A_27a,V5x_2E0)))))))))) -> (all V0t_2E0 all V1s_2E0 all V2r_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eposet_2Efunction_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,A_27b),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_2Ebool),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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0)))))))) # label(thm_2Eposet_2Epointwise__lift__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1991 (all A_27a all V0s_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),V0s_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,V3y_2E0))),s(A_27a,V2x_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Etop_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(A_27a,V2x_2E0)))))) # label(thm_2Eposet_2Etop__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1992 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1993 (all A_27a all V0p_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Ecomplete__down) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1994 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))))),c_2Eposet_2Epointwise__lift_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Epointwise__lift_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1995 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))))),c_2Eposet_2Epointwise__lift_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Epointwise__lift_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1996 (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]. 7.43/7.40 1997 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) & s(A_27a,V3x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0))) & (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4y_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)))))))) # label(thm_2Eposet_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1998 (all A_27a all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V0s_2E0)) # label(thm_2Eposet_2Ecarrier__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 1999 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Elfp_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Elfp_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2000 (all A_27a all F0_2E0 ((all V0s_2E0 all V2p_2E0 all V4j_2E0 (p(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(A_27a,V4j_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4j_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4j_2E0)))))) -> (all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V2p_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Elub__pred) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2001 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(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_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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Elub_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Elub_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2002 (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]. 7.43/7.40 2003 (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(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_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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eposet_2Efunction_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_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_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_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Efunction_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2004 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,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_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2005 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eknaster__tarski__lfp) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2006 (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]. 7.43/7.40 2007 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(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_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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Eglb_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Eglb_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2008 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Edown__continuous_2E2(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Edown__continuous_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Edown__continuous_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2009 (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]. 7.43/7.40 2010 (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]. 7.43/7.40 2011 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V0s_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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))) # label(thm_2Eposet_2Eposet__refl) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2012 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V3x_2E0))))) & (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eknaster__tarski) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2013 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eposet__nonempty) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2014 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V0s_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,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,V3y_2E0))),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) -> s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0))) # label(thm_2Eposet_2Eposet__antisym) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2015 (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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Ebottom_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Ebottom_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Ebottom_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2016 (all A_27a all V0p_2E0 all V1f_2E0 all V2x_2E0 all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V3x_27_2E0)))) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0))) # label(thm_2Eposet_2Elfp__unique) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2017 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 all V3y_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V0s_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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,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,V3y_2E0))),s(A_27a,V4z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V4z_2E0)))))) # label(thm_2Eposet_2Eposet__trans) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2018 (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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Eposet_2Erelation_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Erelation_2E1(s(tyop_2Epair_2Eprod(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_2Eposet_2Erelation_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2019 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Econtinuous_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Econtinuous_2E2(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Econtinuous_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2020 (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]. 7.43/7.40 2021 (all A_27a all X0_2E0 all 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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Ebool)),c_2Eposet_2Echain_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Echain_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2022 (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]. 7.43/7.40 2023 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(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)),X1_2E0))) = s(tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),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)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2024 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Etop_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Eposet_2Ecomplete__top) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2025 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Ecarrier_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(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_2Eposet_2Ecarrier_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2026 (all A_27a all F0_2E0 ((all V0s_2E0 all V3c_2E0 all V2f_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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(A_27a,V5y_2E0)))) <-> (exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(A_27a,V6z_2E0)))) & s(A_27a,V5y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V6z_2E0))))))) -> (all V0s_2E0 all V1r_2E0 all V2f_2E0 ((all V3c_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V3c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V3c_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eup__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0)))))))) # label(thm_2Eposet_2Eup__continuous__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2027 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) <-> (all V1c_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V2x_2E0))))) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V3x_2E0))))))))) # label(thm_2Eposet_2Ecomplete__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2028 (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(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(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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eposet_2Efunction_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,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(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,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Efunction_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2029 (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]. 7.43/7.40 2030 (all A_27a all V0p_2E0 all V1f_2E0 all V2x_2E0 all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V3x_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> s(A_27a,V3x_27_2E0) = s(A_27a,V2x_2E0))) # label(thm_2Eposet_2Egfp__unique) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2031 (all A_27a all V0s_2E0 all V1r_2E0 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_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Erelation_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) # label(thm_2Eposet_2Erelation__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2032 (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]. 7.43/7.40 2033 (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]. 7.43/7.40 2034 (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]. 7.43/7.40 2035 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ebottom_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Eposet_2Ecomplete__bottom) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2036 (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]. 7.43/7.40 2037 (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]. 7.43/7.40 2038 (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]. 7.43/7.40 2039 (all A_27a all V0s_2E0 all V1r_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),V2p_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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,V4y_2E0))),s(A_27a,V3x_2E0)))))) & (all V5z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V5z_2E0)))) & (all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_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)),V1r_2E0),s(A_27a,V6y_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V2p_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Elub__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2040 (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,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Egfp_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Egfp_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2041 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(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_2Eposet_2Eposet_2E0),s(tyop_2Epair_2Eprod(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_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(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_2Eposet_2Eposet_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2042 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0)))))))))) # label(thm_2Eposet_2Efunction__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2043 (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]. 7.43/7.40 2044 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) & s(A_27a,V3x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0))) & (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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,V4y_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_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,V4y_2E0))),s(A_27a,V3x_2E0)))))))) # label(thm_2Eposet_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2045 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Eup__continuous_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Eup__continuous_2E2(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Eup__continuous_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2046 (all A_27a all F0_2E0 ((all V0s_2E0 all V3c_2E0 all V2f_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6z_2E0)))) & s(A_27a,V5y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V6z_2E0))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(A_27a,V5y_2E0)))))) -> (all V0s_2E0 all V1r_2E0 all V2f_2E0 ((all V3c_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V3c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),V3c_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Edown__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0)))))))) # label(thm_2Eposet_2Edown__continuous__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2047 (all A_27a all A_27b all V0p_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))))))) # label(thm_2Eposet_2Ecomplete__pointwise) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2048 (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),c_2Eposet_2Efunction_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,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_27b,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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eposet_2Efunction_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Efunction_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.40 2049 (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]. 7.43/7.40 2050 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Emonotonic_2E0),s(tyop_2Epair_2Eprod(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_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Emonotonic_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2051 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) & (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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,V2x_2E0))),s(A_27a,V3y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ebottom_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(A_27a,V2x_2E0)))))) # label(thm_2Eposet_2Ebottom__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2052 (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]. 7.43/7.41 2053 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_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)),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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4x_2E0)))) -> s(A_27a,V5y_2E0) = s(A_27a,V4x_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),V0s_2E0),s(A_27a,V7y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)),V1r_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)),V1r_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),V0s_2E0),s(A_27a,V6x_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,V6x_2E0))),s(A_27a,V8z_2E0)))))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,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,V3x_2E0)))))) & (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eposet__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2054 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eknaster__tarski__gfp) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2055 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(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_2Eposet_2Ecomplete_2E0),s(tyop_2Epair_2Eprod(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_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(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_2Eposet_2Ecomplete_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2056 (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]. 7.43/7.41 2057 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Etop_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Etop_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Etop_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2058 (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]. 7.43/7.41 2059 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2060 (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]. 7.43/7.41 2061 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2062 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2063 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Enumeral_2Etexp__help_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral_2Etexp__help_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2064 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2065 (all V0n_2E0 all V1a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_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_2EEXP_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,c_2Earithmetic_2E_2B_2E2(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))))))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) # label(thm_2Enumeral_2Etexp__help__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2066 (all V0n_2E0 all V1m_2E0 (s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(thm_2Enumeral_2Enumeral__lte) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2067 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(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)),c_2Earithmetic_2EDIVMOD_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIVMOD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2068 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__div2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2069 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__div2_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2070 (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]. 7.43/7.41 2071 (all V0n_2E0 all V1a_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_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V1a_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,V0n_2E0))) # label(thm_2Enumeral_2Eonecount__characterisation) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2072 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2B_2E2(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)))))))))) # label(thm_2Enumeral_2Etexp__help0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2073 (all V0y_2E0 all V1x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) # label(thm_2Enumeral_2Enumeral__MIN) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2074 (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]. 7.43/7.41 2075 (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]. 7.43/7.41 2076 (all V0acc_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0acc_2E0)))) # label(thm_2Enumeral_2Etexp__help__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2077 (all V1n_2E0 all V2acc_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2acc_2E0)))))) # label(thm_2Enumeral_2Etexp__help__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2078 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Enumeral_2Eonecount_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral_2Eonecount_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2079 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2080 (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]. 7.43/7.41 2081 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Enumeral_2Enumeral__add) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2082 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) # label(thm_2Enumeral_2Enumeral__mult) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2083 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Enumeral_2Enumeral__iisuc) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2084 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2085 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_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,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__sub) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2086 (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]. 7.43/7.41 2087 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral_2EiDUB) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2088 (all A_27a ((all V7n_2E0 all V8zf_2E0 all V9bf1_2E0 all V10bf2_2E0 s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7n_2E0))),s(A_27a,V8zf_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V9bf1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V10bf2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V10bf2_2E0),s(tyop_2Enum_2Enum,V7n_2E0)))) & (all V3n_2E0 all V4zf_2E0 all V5bf1_2E0 all V6bf2_2E0 s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V4zf_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5bf1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V6bf2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5bf1_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) & (all V0zf_2E0 all V1bf1_2E0 all V2bf2_2E0 s(A_27a,V0zf_2E0) = s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(A_27a,V0zf_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1bf1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2bf2_2E0)))))) # label(thm_2Enumeral_2EiBIT__cases) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2089 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EFACT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EFACT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2090 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2091 (all A_27a all V0x_2E0 all V1n_2E0 all V2f_2E0 (s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(A_27a,V0x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V0x_2E0))))) & s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V0x_2E0))))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(A_27a,V0x_2E0))) & s(A_27a,V0x_2E0) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V0x_2E0))))) # label(thm_2Enumeral_2Enumeral__funpow) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2092 (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]. 7.43/7.41 2093 (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]. 7.43/7.41 2094 (all V0n_2E0 all V1m_2E0 ((s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) <-> s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0)) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) <-> s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral_2Enumeral__eq) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2095 (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]. 7.43/7.41 2096 (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]. 7.43/7.41 2097 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2098 (all X0_2E0 all X1_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)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2099 (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_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2100 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = 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,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))))) # label(thm_2Enumeral_2Enumeral__fact_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2101 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_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,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))))))) # label(thm_2Enumeral_2Enumeral__fact_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2102 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumeral_2Einternal__mult__characterisation) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2103 (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]. 7.43/7.41 2104 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.43/7.41 2105 (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_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2106 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiiSUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2107 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral_2Enumeral__suc_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2108 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral_2Enumeral__suc_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2109 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)))),c_2Enumeral_2EiBIT__cases_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X3_2E0)))) # label(arityeq4_2Ec_2Enumeral_2EiBIT__cases_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2110 (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]. 7.43/7.41 2111 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2112 (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]. 7.43/7.41 2113 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMAX_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2114 (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_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2115 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,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)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2116 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,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_2Enumeral_2EiSUB_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumeral_2EiSUB_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2117 (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]. 7.43/7.41 2118 (all F3_2E0 all F0_2E0 all F4_2E0 all F1_2E0 all F5_2E0 all F2_2E0 ((all V10n_2E0 all V13m_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V13m_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)),F3_2E0),s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,V13m_2E0)))) -> ((all V3n_2E0 all V5m_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V5m_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)),F0_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V5m_2E0)))) -> ((all V3n_2E0 all V8m_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)),F4_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V8m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V8m_2E0)))))) -> ((all V10n_2E0 all V12m_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)),F1_2E0),s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,V12m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V12m_2E0)))))) -> ((all V10n_2E0 all V15m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V15m_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)),F5_2E0),s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,V15m_2E0)))) -> ((all V3n_2E0 all V6m_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)),F2_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V6m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V6m_2E0)))))) -> (all V0b_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)) & (all V2b_2E0 all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2b_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),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)),F0_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),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)),F2_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),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)),F2_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),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)),F4_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V2b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4x_2E0)))) & (all V9b_2E0 all V10n_2E0 all V11x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V9b_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V11x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),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)),F1_2E0),s(tyop_2Enum_2Enum,V10n_2E0))),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)),F3_2E0),s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V11x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),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)),F3_2E0),s(tyop_2Enum_2Enum,V10n_2E0))),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)),F5_2E0),s(tyop_2Enum_2Enum,V10n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V9b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,V11x_2E0))))))))))) # label(thm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2119 (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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2120 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral_2EiSQR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2121 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral_2EiZ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2122 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiDUB_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2123 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2124 (all V5n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2125 (all V6n_2E0 all V7m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V7m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2126 (all V8n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V8n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2127 (all V9n_2E0 s(tyop_2Enum_2Enum,V9n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V9n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2128 (all V12n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V12n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2129 (all V13n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V13n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2130 (all V14n_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_2EEXP_2E2(s(tyop_2Enum_2Enum,V14n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2131 (all V15n_2E0 all V16m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V15n_2E0),s(tyop_2Enum_2Enum,V16m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V15n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V16m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2132 (all V17n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V17n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2133 (all V18n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V18n_2E0))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V18n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2134 (all V20n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V20n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,V20n_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2135 (all V21n_2E0 all V22m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V21n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V22m_2E0))) <-> s(tyop_2Enum_2Enum,V22m_2E0) = s(tyop_2Enum_2Enum,V21n_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2136 (all V24n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V24n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V24n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2137 (all V27n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V27n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2138 (all V28n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V28n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V28n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2139 (all V31n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V31n_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2140 (all V33n_2E0 all V34m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V33n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V34m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V33n_2E0),s(tyop_2Enum_2Enum,V34m_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2141 (all V40n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V40n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V40n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2142 (all V39n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V39n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V39n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2143 (all V37n_2E0 all V38m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V37n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V38m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V38m_2E0),s(tyop_2Enum_2Enum,V37n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2144 (all V36n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V36n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V36n_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2145 (all V35n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V35n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2146 (all V32n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V32n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V32n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2147 (all V29n_2E0 all V30m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V30m_2E0),s(tyop_2Enum_2Enum,V29n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V29n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V30m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2148 (all V25n_2E0 all V26m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V26m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V25n_2E0),s(tyop_2Enum_2Enum,V26m_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2149 (all V23n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V23n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2150 (all V19n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,V19n_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2151 (all V10n_2E0 all V11m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V11m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2152 (all V4n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2153 (all V2n_2E0 all V3m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V3m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2154 (all V1n_2E0 s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2155 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2156 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2157 (all V2m_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_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,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2158 (all V6m_2E0 all V7n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V6m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V6m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2159 (all V4m_2E0 all V5n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2160 (all A_27a all V0zf_2E0 all V1b1f_2E0 all V2b2f_2E0 exists V3f_2E0 ((all V5n_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)),V2b2f_2E0),s(tyop_2Enum_2Enum,V5n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V5n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V5n_2E0)))))) & (all V4n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_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)),V1b1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) & s(A_27a,V0zf_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) # label(thm_2Enumeral_2Ebit__initiality) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2161 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2x_2E0)))) # label(thm_2Enumeral_2Eonecount__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2162 (all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4x_2E0)))) # label(thm_2Enumeral_2Eonecount__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2163 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Enumeral_2Eonecount__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2164 (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]. 7.43/7.41 2165 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = 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,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2166 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2167 (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]. 7.43/7.41 2168 (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_2Enumeral_2Einternal__mult_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral_2Einternal__mult_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2169 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiSQR_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiSQR_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2170 (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]. 7.43/7.41 2171 (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]. 7.43/7.41 2172 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__evenodd) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2173 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2174 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_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,V0n_2E0))) # label(thm_2Enumeral_2Eexactlog__characterisation) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2175 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2176 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2177 (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]. 7.43/7.41 2178 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Earithmetic_2Efindq_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_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)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2Efindq_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2179 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)))),c_2Enumeral_2EiBIT__cases_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3_2E0)))) # label(arityeq4_2Ec_2Enumeral_2EiBIT__cases_2E4_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2180 (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]. 7.43/7.41 2181 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Enumeral_2EiDUB__removal) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2182 (all F0_2E0 ((all V1a_2E0 all V0m_2E0 all V2n_2E0 all V3q_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V3q_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3q_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),F0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3q_2E0)))) -> (all V0m_2E0 all V1a_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)))) -> s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_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,V1a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_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,V0m_2E0),s(tyop_2Enum_2Enum,V2n_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,V0m_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),F0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V2n_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,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))))))))) # label(thm_2Enumeral_2Edivmod__POS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2183 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Enumeral_2EDIV2__BIT1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2184 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2185 (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_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.41 2186 (all F1_2E0 all F0_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) <-> s(tyop_2Enum_2Enum,V2x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) -> ((all V2x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)) & (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Enumeral_2Eexactlog__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2187 (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]. 7.43/7.42 2188 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),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,c_2Earithmetic_2EEXP_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,c_2Enum_2E0_2E0))))) # label(thm_2Enumeral_2ETWO__EXP__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2189 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__pre_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2190 (all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2191 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2192 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epair_2ESND_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_2ESND_2E0),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]. 7.43/7.42 2193 (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]. 7.43/7.42 2194 (all V0x_2E0 all V1b_2E0 all V2n_2E0 all V3m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0))) # label(thm_2Enumeral_2EiSUB__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2195 (all V0n_2E0 all V1acc_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1acc_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1acc_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V1acc_2E0))))) # label(thm_2Enumeral_2Enumeral__texp__help) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2196 (all V0P_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)))) -> 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_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_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_2Earithmetic_2EBIT1_2E1(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_2Earithmetic_2EZERO_2E0)))) -> (all V3n_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_2Enumeral_2Ebit__induction) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2197 (all V0n_2E0 all V1m_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Enumeral_2Enumeral__lt) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2198 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiZ_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiZ_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2199 (all V0y_2E0 all V1x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) & s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,V1x_2E0))) # label(thm_2Enumeral_2Enumeral__MAX) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2200 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eexactlog_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2Eexactlog_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2201 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumeral_2EiiSUC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2202 (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]. 7.43/7.42 2203 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) # label(thm_2Enumeral_2Enumeral__exp_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2204 (all V1n_2E0 all V2m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2m_2E0)))))) # label(thm_2Enumeral_2Enumeral__exp_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2205 (all V3n_2E0 all V4m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4m_2E0)))))) # label(thm_2Enumeral_2Enumeral__exp_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2206 (all F1_2E0 all F0_2E0 all F3_2E0 all F2_2E0 ((all V0y_2E0 all V1x_2E0 all V4m_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V4m_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))),s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0)))))))) -> ((all V1x_2E0 all V0y_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))),s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V3n_2E0)))) -> ((all V5m_2E0 all V0y_2E0 all V1x_2E0 all V6n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))),s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),s(tyop_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V6n_2E0)))) -> ((all V0y_2E0 all V1x_2E0 all V5m_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F2_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V5m_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),s(tyop_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0)))))))) -> (all V0y_2E0 all V1x_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F2_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2207 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2ELEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2208 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2209 (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]. 7.43/7.42 2210 (all A_27a all V0s_2E0 all V1f_2E0 all V2G_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0s_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(A_27a,V0s_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0s_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0s_2E0)))))) # label(thm_2Ewhile_2EOWHILE__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2211 (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]. 7.43/7.42 2212 (all V0p_2E0 ((exists 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_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_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,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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,V2n_2E0)))))))) # label(thm_2Ewhile_2ELEAST__EXISTS__IMP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2213 (all V0p_2E0 ((exists 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))))) <-> (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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,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_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0)))))))) # label(thm_2Ewhile_2ELEAST__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2214 (all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_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_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ewhile_2ELEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2215 (all V0Q_2E0 all V1P_2E0 (((all V2n_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))))) & (all 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)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Ewhile_2EOLEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2216 (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]. 7.43/7.42 2217 (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]. 7.43/7.42 2218 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(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_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ewhile_2EHOARE__SPEC_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_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EHOARE__SPEC_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2219 (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]. 7.43/7.42 2220 (all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,V1x_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_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ewhile_2EFULL__LEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2221 (all V0P_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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,V1m_2E0)))))) # label(thm_2Ewhile_2ELESS__LEAST) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2222 (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]. 7.43/7.42 2223 (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,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ewhile_2EWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ewhile_2EWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ewhile_2EWHILE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2224 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2225 (all F1_2E0 all F0_2E0 ((all V0x_2E0 all 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)),F1_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) <-> s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,V2n_2E0))) -> ((all V0x_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(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)),F1_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))))))) # label(thm_2Ewhile_2ELEAST__EQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2226 (all V0P_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))))) <-> s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) # label(thm_2Ewhile_2EOLEAST__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2227 (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]. 7.43/7.42 2228 (all A_27a all V0P_2E0 all V1G_2E0 all V2f_2E0 ((all V3s_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(A_27a,V3s_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)),V0P_2E0),s(A_27a,V3s_2E0))),s(A_27a,V3s_2E0)))))) & (all V4s1_2E0 all V5s2_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)),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4s1_2E0))))),s(A_27a,V5s2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(A_27a,V4s1_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)),V0P_2E0),s(A_27a,V4s1_2E0))),s(A_27a,V5s2_2E0)))))) -> (all V6s1_2E0 all V7s2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7s2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V6s1_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)),V0P_2E0),s(A_27a,V6s1_2E0))),s(A_27a,V7s2_2E0)))))))) # label(thm_2Ewhile_2EOWHILE__IND) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2229 (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]. 7.43/7.42 2230 (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_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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ewhile_2EWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EWHILE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2231 (all A_27a all F1_2E0 all F0_2E0 ((all V0P_2E0 all V2B_2E0 all V6s_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V6s_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V6s_2E0)))) <-> p(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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0))),s(A_27a,V6s_2E0)))))) -> ((all V0P_2E0 all V2B_2E0 all V5s_2E0 (p(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0))),s(A_27a,V5s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5s_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V5s_2E0)))))) -> (all V0P_2E0 all V1R_2E0 all V2B_2E0 all V3C_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 V4s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V4s_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),V3C_2E0),s(A_27a,V4s_2E0))))),s(A_27a,V4s_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V3C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ewhile_2EWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V3C_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0)))))))))))) # label(thm_2Ewhile_2EWHILE__RULE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2232 (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]. 7.43/7.42 2233 (all V0Q_2E0 all V1P_2E0 ((exists V2n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) & (all V3n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_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)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Ewhile_2ELEAST__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2234 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.43/7.42 2235 (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]. 7.43/7.42 2236 (all A_27a all V0s_2E0 all V1f_2E0 all V2G_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0s_2E0))) <-> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V0s_2E0))))))))) # label(thm_2Ewhile_2EOWHILE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2237 (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]. 7.43/7.42 2238 (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]. 7.43/7.42 2239 (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]. 7.43/7.42 2240 (all A_27a all A_27b all V0P_2E0 all V1C_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1C_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))) <-> (all V3s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1C_2E0),s(A_27a,V3s_2E0)))))))))) # label(thm_2Ewhile_2EHOARE__SPEC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2241 (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]. 7.43/7.42 2242 (all A_27a all V0P_2E0 all V1G_2E0 all V2f_2E0 all V3s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3s_2E0)))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_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)))) -> 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(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) -> (all V5s_27_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3s_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5s_27_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5s_27_2E0)))))))) # label(thm_2Ewhile_2EOWHILE__INV__IND) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2243 (all V0P_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Ewhile_2ELEAST__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2244 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2ESOME_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2245 (all F0_2E0 ((all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0))))) # label(thm_2Ewhile_2ELEAST__T) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2246 (all A_27a all V0P_2E0 all V1g_2E0 exists V2f_2E0 all V3x_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(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,V3x_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(A_27a,A_27a),V1g_2E0),s(A_27a,V3x_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0)))) # label(thm_2Ewhile_2EITERATION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2247 (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]. 7.43/7.42 2248 (all A_27a all V0s_27_2E0 all V1s_2E0 all V2f_2E0 all V3G_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1s_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0s_27_2E0))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(A_27a,V0s_27_2E0)))))) # label(thm_2Ewhile_2EOWHILE__ENDCOND) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2249 (all A_27a all F0_2E0 all F1_2E0 ((all V0G_2E0 all V1f_2E0 all V2s_2E0 ((exists V3n_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(A_27a,V2s_2E0)))))) -> ((all V0G_2E0 all V1f_2E0 all V2s_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(A_27a,V2s_2E0))),s(tyop_2Enum_2Enum,V4n_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0),s(A_27a,V2s_2E0)))))))) -> (all V0G_2E0 all V1f_2E0 all V2s_2E0 s(tyop_2Eoption_2Eoption(A_27a),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(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(A_27a,V2s_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(A_27a,V2s_2E0))))),s(A_27a,V2s_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2s_2E0))))))) # label(thm_2Ewhile_2EOWHILE__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2250 (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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ewhile_2EWHILE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EWHILE_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2251 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ewhile_2EOLEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2EOLEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2252 (all F0_2E0 all F1_2E0 ((all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) <-> (exists 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))))))) -> ((all V0P_2E0 all V2n_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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> (all V0P_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Ewhile_2EOLEAST__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2253 (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]. 7.43/7.42 2254 (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]. 7.43/7.42 2255 (all A_27a all V0B_2E0 all V1C_2E0 all V2R_2E0 ((all V3s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(A_27a,V3s_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,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1C_2E0),s(A_27a,V3s_2E0))))),s(A_27a,V3s_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)))) -> (all V4P_2E0 ((all V5s_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(A_27a,V5s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1C_2E0),s(A_27a,V5s_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V5s_2E0)))))) -> (all V6v_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V6v_2E0))))))))) # label(thm_2Ewhile_2EWHILE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2256 (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]. 7.43/7.42 2257 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2258 (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]. 7.43/7.42 2259 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),c_2Ewhile_2EOWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EOWHILE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2260 (all V0n_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & (all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))) <-> s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Ewhile_2EOLEAST__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2261 (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]. 7.43/7.42 2262 (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]. 7.43/7.42 2263 (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]. 7.43/7.42 2264 (all F3_2E0 all F2_2E0 all F1_2E0 all F0_2E0 ((all V4n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) -> ((all V3n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> ((all V0x_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,V0x_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)),F1_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> ((all V0x_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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0x_2E0))) -> (all V0x_2E0 (s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(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)),F1_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))) & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_2E0))) & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))))))))) # label(thm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2265 (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]. 7.43/7.42 2266 (all A_27a all V0s_27_2E0 all V1s_2E0 all V2f_2E0 all V3G_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0s_27_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1s_2E0))) -> s(A_27a,V0s_27_2E0) = s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1s_2E0))))) # label(thm_2Ewhile_2EOWHILE__WHILE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2267 (all A_27a all V0P_2E0 all V1g_2E0 all V2x_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(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,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,V2x_2E0))))),s(A_27a,V2x_2E0))) = s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,V2x_2E0)))) # label(thm_2Ewhile_2EWHILE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2268 (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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ewhile_2EHOARE__SPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EHOARE__SPEC_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2269 (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]. 7.43/7.42 2270 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2271 (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]. 7.43/7.42 2272 (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]. 7.43/7.42 2273 (all V0b_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2EbasicSize_2Ebool__size__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2274 (all A_27a all A_27b all 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))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2275 (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]. 7.43/7.42 2276 (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]. 7.43/7.42 2277 (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]. 7.43/7.42 2278 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V1g_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0))),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0),s(A_27b,V3y_2E0)))))) -> (all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2EbasicSize_2Epair__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0)))))) # label(thm_2EbasicSize_2Epair__size__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2279 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Enum_2Enum),c_2EbasicSize_2Eone__size_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2EbasicSize_2Eone__size_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2280 (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]. 7.43/7.42 2281 (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]. 7.43/7.42 2282 (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]. 7.43/7.42 2283 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size_2E1(s(tyop_2Eone_2Eone,V0x_2E0)))) # label(thm_2EbasicSize_2Eone__size__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2284 (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]. 7.43/7.42 2285 (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]. 7.43/7.42 2286 (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]. 7.43/7.42 2287 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2288 (all A_27a all A_27b all 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))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2289 (all A_27a all A_27b ((all V3f_2E0 all V4g_2E0 all V5y_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Esum__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V5y_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4g_2E0),s(A_27b,V5y_2E0)))) & (all V0f_2E0 all V1g_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Esum__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0)))))))) # label(thm_2EbasicSize_2Esum__size__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2290 (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]. 7.43/7.42 2291 (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]. 7.43/7.42 2292 (all X0_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),c_2EbasicSize_2Ebool__size_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2EbasicSize_2Ebool__size_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2293 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2294 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2EbasicSize_2Epair__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum))),c_2EbasicSize_2Epair__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2EbasicSize_2Epair__size_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2295 (all A_27a ((all V1f_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Eoption__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))) & (all V0f_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Eoption__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2EbasicSize_2Eoption__size__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2296 (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]. 7.43/7.42 2297 (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]. 7.43/7.42 2298 (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]. 7.43/7.42 2299 (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]. 7.43/7.42 2300 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.42 2301 (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]. 7.43/7.42 2302 (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]. 7.43/7.42 2303 (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]. 7.43/7.43 2304 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Eoption__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum)),c_2EbasicSize_2Eoption__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2EbasicSize_2Eoption__size_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2305 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Esum__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Enum_2Enum))),c_2EbasicSize_2Esum__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2EbasicSize_2Esum__size_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2306 (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]. 7.43/7.43 2307 (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]. 7.43/7.43 2308 (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]. 7.43/7.43 2309 (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]. 7.43/7.43 2310 (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_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2311 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Edivides_2EALL__DIVIDES__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2312 (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_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EINDEX__LESS__PRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2313 (all V0a_2E0 ((all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,V1b_2E0) | s(tyop_2Enum_2Enum,V1b_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,V0a_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(thm_2Edivides_2Eprime__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2314 (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]. 7.43/7.43 2315 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,V1b_2E0))) # label(thm_2Edivides_2EDIVIDES__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2316 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Edivides_2EDIVIDES__LEQ__OR__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2317 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2318 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Edivides_2EPRIMES_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Edivides_2EPRIMES_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2319 (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]. 7.43/7.43 2320 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2321 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Edivides_2EINFINITE__PRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2322 (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]. 7.43/7.43 2323 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2324 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Edivides_2ENOT__LT__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2325 (all V0n_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Edivides_2EPRIMES__NO__GAP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2326 (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_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EZERO__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2327 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_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,V0a_2E0))))) # label(thm_2Edivides_2EONE__DIVIDES__ALL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2328 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_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,V0p_2E0)))))) # label(thm_2Edivides_2EONE__LT__PRIME) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2329 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EFACT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EFACT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2330 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__ADD__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2331 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Edivides_2ELEQ__DIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2332 (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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2333 (all F1_2E0 all F0_2E0 ((all V0a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) <-> s(tyop_2Enum_2Enum,V0a_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 V0a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) <-> s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) -> (all V0a_2E0 all V1b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))))))))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))))) # label(thm_2Edivides_2Ecompute__divides) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2334 (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]. 7.43/7.43 2335 (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]. 7.43/7.43 2336 (all V0n_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,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EONE__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2337 (all 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,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(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)))))))))) # label(thm_2Edivides_2EDIVIDES__ONE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2338 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) -> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Edivides_2Eprime__divides__only__self) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2339 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))))) # label(thm_2Edivides_2EPRIME__POS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2340 (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]. 7.43/7.43 2341 (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]. 7.43/7.43 2342 (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]. 7.43/7.43 2343 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.43/7.43 2344 (all V0a_2E0 all V1b_2E0 ((exists V2q_2E0 s(tyop_2Enum_2Enum,V1b_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Edivides_2Edivides__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2345 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> (exists V1i_2E0 s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Enum_2Enum,V0p_2E0)))) # label(thm_2Edivides_2EPRIMES__ONTO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2346 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Edivides_2Eprime_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Edivides_2Eprime_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2347 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2348 (all V0n_2E0 exists V1i_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0))))))) # label(thm_2Edivides_2EEUCLID__PRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2349 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2350 (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]. 7.43/7.43 2351 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_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)),c_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Edivides_2Edivides_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2352 (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]. 7.43/7.43 2353 (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]. 7.43/7.43 2354 (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_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Edivides_2ELT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2355 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Edivides_2EDIVIDES__LE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2356 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Edivides_2EDIVIDES__REFL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2357 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2358 (all V0n_2E0 exists V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))))) # label(thm_2Edivides_2EEUCLID) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2359 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2360 (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]. 7.43/7.43 2361 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V0b_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2362 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Edivides_2EDIVIDES__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2363 (all F0_2E0 ((all V0n_2E0 all V1p_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)),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1p_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(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)),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Edivides_2EPRIMES__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2364 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2ELEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2365 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) -> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Edivides_2EPRIMES__11) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2366 (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]. 7.43/7.43 2367 (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]. 7.43/7.43 2368 (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]. 7.43/7.43 2369 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Edivides_2EDIVIDES__ADD__2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2370 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) <-> s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_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))))))) # label(thm_2Edivides_2EDIVIDES__MULT__LEFT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2371 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2372 (all V0n_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))))) -> (exists V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Edivides_2EPRIME__FACTOR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2373 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Edivides_2EZERO__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2374 (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]. 7.43/7.43 2375 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__SUB) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2376 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EprimePRIMES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2377 (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]. 7.43/7.43 2378 (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]. 7.43/7.43 2379 (all V0n_2E0 exists V1i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0)))))) & (all V2j_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Enum_2Enum,V1i_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V2j_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Edivides_2ENEXT__LARGER__PRIME) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2380 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) <-> (exists V1i_2E0 s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Enum_2Enum,V0p_2E0)))) # label(thm_2Edivides_2EPRIME__INDEX) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2381 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2382 (all A_27a all F0_2E0 ((all V0z_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0z_2E0)))) -> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))))))) # label(thm_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2383 (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]. 7.43/7.43 2384 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2Edest__rec_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2Edest__rec_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2385 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eind__type_2Erecspace_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2386 (all A_27a all A_27b all V0g_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0)))) -> (all V5P_2E0 ((exists V7x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V7x_2E0))))))) <-> (exists V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5P_2E0),s(A_27a,V6x_2E0))))))) & (all V8a_2E0 all V9b_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V8a_2E0))) = s(A_27b,V9b_2E0) <-> s(A_27a,V8a_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V9b_2E0))))) & (all V2P_2E0 ((all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V4x_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))))))))) # label(thm_2Eind__type_2EISO__USAGE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2387 (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]. 7.43/7.43 2388 (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]. 7.43/7.43 2389 (all A_27a all V0m_2E0 all V1x_2E0 all V2x_27_2E0 (s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJN_2E3(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(A_27a,V2x_27_2E0)))))) # label(thm_2Eind__type_2EINJN) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2390 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2391 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2392 (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]. 7.43/7.43 2393 (all A_27a all V0f_2E0 all V1x_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eind__type_2EINJF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Eind__type_2EINJF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2394 (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]. 7.43/7.43 2395 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMRIGHT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMRIGHT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2396 (all A_27a all F0_2E0 ((all V2r_2E0 all V3n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0))),s(tyop_2Enum_2Enum,V3n_2E0)))) -> (all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0))))))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0)))))) # label(thm_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2397 (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]. 7.43/7.43 2398 (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]. 7.43/7.43 2399 (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]. 7.43/7.43 2400 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,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_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) # label(thm_2Eind__type_2ENUMPAIR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2401 (all A_27a all V0ZRECSPACE_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))) & (all V1c_2E0 all V2i_2E0 all V3r_2E0 ((all V4n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0)))))))) -> (all V5a0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))))))) # label(thm_2Eind__type_2EZRECSPACE__ind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2402 (all A_27a all V0n_2E0 s(A_27a,c_2Eind__type_2EFNIL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(A_27a,c_2Ebool_2EARB_2E0)) # label(thm_2Eind__type_2EFNIL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2403 (all A_27a all V0a1_2E0 all V1a2_2E0 (s(A_27a,V1a2_2E0) = s(A_27a,V0a1_2E0) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,V1a2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,V0a1_2E0))))) # label(thm_2Eind__type_2EINJA__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2404 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2405 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,X0_2E0))) = s(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_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJA_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EINJA_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2406 (all A_27a all V0a_2E0 all V1x_2E0 all V2x_27_2E0 (s(A_27a,V0a_2E0) = s(A_27a,V2x_27_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJA_2E3(s(A_27a,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(A_27a,V2x_27_2E0)))))) # label(thm_2Eind__type_2EINJA) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2407 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMFST_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMFST_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2408 (all A_27a ((all V0a_2E0 all V1f_2E0 s(A_27a,V0a_2E0) = s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V2a_2E0 all V3f_2E0 all V4n_2E0 s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(thm_2Eind__type_2EFCONS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2409 (all A_27a all V0f1_2E0 all V1f2_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1f2_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f1_2E0) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1f2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f1_2E0))))) # label(thm_2Eind__type_2EINJF__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2410 (all A_27a all V0n1_2E0 all V1n2_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,V1n2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,V0n1_2E0))) <-> s(tyop_2Enum_2Enum,V0n1_2E0) = s(tyop_2Enum_2Enum,V1n2_2E0))) # label(thm_2Eind__type_2EINJN__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2411 (all A_27a all V0f1_2E0 all V1f1_27_2E0 all V2f2_2E0 all V3f2_27_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f1_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f2_27_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f2_27_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f2_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f1_27_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0))) # label(thm_2Eind__type_2EINJP__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2412 (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]. 7.43/7.43 2413 (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]. 7.43/7.43 2414 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSND_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMSND_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2415 (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]. 7.43/7.43 2416 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eind__type_2EZRECSPACE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EZRECSPACE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2417 (all A_27a all V0P_2E0 ((all V1c_2E0 all V2i_2E0 all V3r_2E0 ((all V4n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V3r_2E0)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)))) -> (all V5x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V5x_2E0))))))) # label(thm_2Eind__type_2ECONSTR__IND) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2418 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2419 (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_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2420 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eind__type_2EINJP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EINJP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2421 (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_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJN_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EINJN_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2422 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0))) != s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)) # label(thm_2Eind__type_2ECONSTR__BOT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2423 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2424 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Eind__type_2EFCONS_2E3(s(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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eind__type_2EFCONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EFCONS_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2425 (all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2426 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2427 (all V0x1_2E0 all V1y1_2E0 all V2x2_2E0 all V3y2_2E0 (s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x1_2E0),s(tyop_2Enum_2Enum,V1y1_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V2x2_2E0),s(tyop_2Enum_2Enum,V3y2_2E0))) -> s(tyop_2Enum_2Enum,V2x2_2E0) = s(tyop_2Enum_2Enum,V0x1_2E0))) # label(thm_2Eind__type_2ENUMPAIR__INJ__LEMMA) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2428 (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]. 7.43/7.43 2429 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EINJN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2430 (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]. 7.43/7.43 2431 (all A_27a all A_27b all F0_2E0 ((all V1f_2E0 all V4r_2E0 all V5n_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0))),s(tyop_2Enum_2Enum,V5n_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0),s(tyop_2Enum_2Enum,V5n_2E0)))))) -> (all V0Fn_2E0 exists V1f_2E0 all V2c_2E0 all V3i_2E0 all V4r_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V2c_2E0),s(A_27a,V3i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b)))),V0Fn_2E0),s(tyop_2Enum_2Enum,V2c_2E0))),s(A_27a,V3i_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0)))))))) # label(thm_2Eind__type_2ECONSTR__REC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2432 (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]. 7.43/7.43 2433 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V1y_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V0x_2E0))) <-> s(tyop_2Eind__type_2Erecspace(A_27a),V0x_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),V1y_2E0))) # label(thm_2Eind__type_2EDEST__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2434 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eind__type_2EZRECSPACE_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0rep_2E0))))) # label(thm_2Eind__type_2Erecspace__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2435 (all V0b1_2E0 all V1x1_2E0 all V2b2_2E0 all V3x2_2E0 (s(tyop_2Emin_2Ebool,V2b2_2E0) = s(tyop_2Emin_2Ebool,V0b1_2E0) & s(tyop_2Enum_2Enum,V1x1_2E0) = s(tyop_2Enum_2Enum,V3x2_2E0) <-> s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0b1_2E0),s(tyop_2Enum_2Enum,V1x1_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V2b2_2E0),s(tyop_2Enum_2Enum,V3x2_2E0))))) # label(thm_2Eind__type_2ENUMSUM__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2436 (all A_27a all V0ZRECSPACE_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))) & (all V1c_2E0 all V2i_2E0 all V3r_2E0 ((all V4n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0)))))))) -> (all V5a0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))))))) # label(thm_2Eind__type_2EZRECSPACE__strongind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2437 (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_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJA_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJA_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EINJA_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2438 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EINJF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2439 (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]. 7.43/7.43 2440 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0))) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)) # label(thm_2Eind__type_2EZCONSTR__ZBOT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2441 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))) <-> (all V1ZRECSPACE_27_2E0 ((all V2a0_2E0 ((exists V3c_2E0 exists V4i_2E0 exists V5r_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V3c_2E0),s(A_27a,V4i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V5r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a0_2E0) & (all V6n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V1ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V5r_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))))))) | s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a0_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V1ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a0_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V1ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))))))) # label(thm_2Eind__type_2EZRECSPACE__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2442 (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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2443 (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]. 7.43/7.43 2444 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),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,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2445 (all A_27a all F0_2E0 ((all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V0x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0)))))) # label(thm_2Eind__type_2EISO__REFL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2446 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2447 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2448 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2449 (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]. 7.43/7.43 2450 (all A_27A all A_27B all A_27C all V0P_2E0 ((all V1x1_2E0 all V2y1_2E0 all V3x2_2E0 all V4y2_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)),V0P_2E0),s(A_27A,V3x2_2E0))),s(A_27B,V4y2_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)),V0P_2E0),s(A_27A,V1x1_2E0))),s(A_27B,V2y1_2E0))) <-> s(A_27B,V2y1_2E0) = s(A_27B,V4y2_2E0) & s(A_27A,V3x2_2E0) = s(A_27A,V1x1_2E0))) -> (exists V5X_2E0 exists V6Y_2E0 all V7x_2E0 all V8y_2E0 (s(A_27A,V7x_2E0) = s(A_27A,app_2E2(s(tyop_2Emin_2Efun(A_27C,A_27A),V5X_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)),V0P_2E0),s(A_27A,V7x_2E0))),s(A_27B,V8y_2E0))))) & s(A_27B,V8y_2E0) = s(A_27B,app_2E2(s(tyop_2Emin_2Efun(A_27C,A_27B),V6Y_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)),V0P_2E0),s(A_27A,V7x_2E0))),s(A_27B,V8y_2E0))))))))) # label(thm_2Eind__type_2EINJ__INVERSE2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2451 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),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_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2452 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eind__type_2ENUMLEFT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMLEFT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2453 (all A_27a ((all V1r_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) & (all V0a_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V0a_2E0))))) = s(tyop_2Eind__type_2Erecspace(A_27a),V0a_2E0)))) # label(thm_2Eind__type_2Erecspace__repfns) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2454 (all A_27a all V0c1_2E0 all V1i1_2E0 all V2r1_2E0 all V3c2_2E0 all V4i2_2E0 all V5r2_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V0c1_2E0),s(A_27a,V1i1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r1_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V3c2_2E0),s(A_27a,V4i2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V5r2_2E0))) <-> s(A_27a,V1i1_2E0) = s(A_27a,V4i2_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r1_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V5r2_2E0) & s(tyop_2Enum_2Enum,V3c2_2E0) = s(tyop_2Enum_2Enum,V0c1_2E0))) # label(thm_2Eind__type_2ECONSTR__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2455 (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]. 7.43/7.43 2456 (all A_27a all F0_2E0 ((all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> (all V0n_2E0 all V1f_2E0 all V2a_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(A_27a,V2a_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(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))))))))))) = s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Eind__type_2EFCONS__DEST) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2457 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0c_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,V1i_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0)))))))) # label(thm_2Eind__type_2EZCONSTR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2458 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Efun(A_27a,tyop_2Emin_2Ebool))),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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))),c_2Eind__type_2EZCONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EZCONSTR_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2459 (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]. 7.43/7.43 2460 (all A_27a all X0_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2Emk__rec_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2Emk__rec_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2461 (all A_27a all V0a0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0a0_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0a0_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0) | (exists V1c_2E0 exists V2i_2E0 exists V3r_2E0 ((all V4n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0a0_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0))))))) # label(thm_2Eind__type_2EZRECSPACE__cases) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2462 (all A_27a all A_27b all A_27c all A_27d all F1_2E0 all F0_2E0 ((all V0g_27_2E0 all V3f_2E0 all V6h_2E0 all V7a_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6h_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(A_27a,V7a_2E0))))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V6h_2E0))),s(A_27a,V7a_2E0)))) -> ((all V1g_2E0 all V2f_27_2E0 all V4h_2E0 all V5a_27_2E0 s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0))),s(A_27c,V5a_27_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0),s(A_27c,V5a_27_2E0)))))))) -> (all V0g_27_2E0 all V1g_2E0 all V2f_27_2E0 all V3f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0))))))))))) # label(thm_2Eind__type_2EISO__FUN) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2463 (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]. 7.43/7.43 2464 (all V0b_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),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,V1x_2E0))))),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,V1x_2E0)))))) # label(thm_2Eind__type_2ENUMSUM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2465 (all V0x_2E0 all V1y_2E0 (s(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) = s(tyop_2Emin_2Ebool,V0x_2E0) & s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))))) # label(thm_2Eind__type_2ENUMSUM__DEST) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2466 (all V0x1_2E0 all V1y1_2E0 all V2x2_2E0 all V3y2_2E0 (s(tyop_2Enum_2Enum,V2x2_2E0) = s(tyop_2Enum_2Enum,V0x1_2E0) & s(tyop_2Enum_2Enum,V1y1_2E0) = s(tyop_2Enum_2Enum,V3y2_2E0) <-> s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V2x2_2E0),s(tyop_2Enum_2Enum,V3y2_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x1_2E0),s(tyop_2Enum_2Enum,V1y1_2E0))))) # label(thm_2Eind__type_2ENUMPAIR__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2467 (all A_27a (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))) & (all V0c_2E0 all V1i_2E0 all V2r_2E0 ((all V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0)))))))))) # label(thm_2Eind__type_2EZRECSPACE__rules) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2468 (all A_27a s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))) # label(thm_2Eind__type_2EBOTTOM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2469 (all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) & s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))))) # label(thm_2Eind__type_2ENUMPAIR__DEST) # label(axiom) # label(non_clause). [assumption]. 7.43/7.43 2470 (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]. 7.43/7.43 2471 (all A_27a all V0f1_2E0 all V1f2_2E0 all V2x_2E0 all V3x_27_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJP_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0),s(tyop_2Enum_2Enum,V2x_2E0),s(A_27a,V3x_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(s(tyop_2Enum_2Enum,V2x_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)),V0f1_2E0),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(A_27a,V3x_27_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)),V1f2_2E0),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(A_27a,V3x_27_2E0)))))) # label(thm_2Eind__type_2EINJP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2472 (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]. 7.43/7.44 2473 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0)))) -> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0)))) # label(thm_2Eind__type_2EMK__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2474 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0)))) <-> (all 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_27b,A_27a),V1g_2E0),s(A_27b,V2x_2E0))))) = s(A_27b,V2x_2E0)) & (all V3y_2E0 s(A_27a,V3y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0)))))))) # label(thm_2Eind__type_2EISO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2475 (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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eind__type_2EINJP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJP_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Eind__type_2EINJP_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2476 (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_2Eind__type_2ENUMPAIR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2ENUMPAIR_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2477 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Eind__type_2EFNIL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(A_27a,c_2Eind__type_2EFNIL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EFNIL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2478 (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]. 7.43/7.44 2479 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eind__type_2EINJF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Enum_2Enum,X1_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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EINJF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2480 (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_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eind__type_2ENUMSUM_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2ENUMSUM_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2481 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Egcd_2EGCD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2482 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) & (all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Egcd_2ELCM__IS__LEAST__COMMON__MULTIPLE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2483 (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]. 7.43/7.44 2484 (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]. 7.43/7.44 2485 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Egcd_2EGCD__ADD__L) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2486 (all V0b_2E0 all V1a_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) # label(thm_2Egcd_2ELCM__COMM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2487 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2488 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) & s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_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_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2EL__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2489 (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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2490 (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_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Edivides_2Edivides_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2491 (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]. 7.43/7.44 2492 (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Egcd_2ELCM__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2493 (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]. 7.43/7.44 2494 (all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0)))) # label(thm_2Egcd_2EGCD__ADD__R__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2495 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Egcd_2EGCD__ADD__R__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2496 (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Egcd_2Egcd__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2497 (all V2y_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2y_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2y_2E0))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V3x_2E0)))))))) # label(thm_2Egcd_2Egcd__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2498 (all V0y_2E0 s(tyop_2Enum_2Enum,V0y_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) # label(thm_2Egcd_2Egcd__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2499 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> (exists V2p_2E0 exists V3q_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Egcd_2ELINEAR__GCD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2500 (all V0m_2E0 all V1n_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Egcd_2EGCD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2501 (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]. 7.43/7.44 2502 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2503 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Edivides_2Eprime_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Edivides_2Eprime_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2504 (all V0P_2E0 ((all V1y_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_2E0_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))) & (all V4x_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,V4x_2E0))),s(tyop_2Enum_2Enum,V4x_2E0))))) & (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V5x_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,V5x_2E0))),s(tyop_2Enum_2Enum,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V6y_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,V5x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V6y_2E0)))))))) & (all V2x_2E0 all V3y_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,V2x_2E0))),s(tyop_2Enum_2Enum,V3y_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,V3y_2E0))),s(tyop_2Enum_2Enum,V2x_2E0)))))) -> (all V7m_2E0 all V8n_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,V7m_2E0))),s(tyop_2Enum_2Enum,V8n_2E0))))))) # label(thm_2Egcd_2EGCD__SUCfree__ind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2505 (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]. 7.43/7.44 2506 (all V0P_2E0 ((all V3x_2E0 all V4y_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4y_2E0),s(tyop_2Enum_2Enum,V3x_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_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V4y_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4y_2E0))))))) & (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4y_2E0),s(tyop_2Enum_2Enum,V3x_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,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V4y_2E0),s(tyop_2Enum_2Enum,V3x_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,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4y_2E0)))))))) & (all V2x_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,V2x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) & (all V1y_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_2E0_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))) -> (all V5v_2E0 all V6v1_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,V5v_2E0))),s(tyop_2Enum_2Enum,V6v1_2E0))))))) # label(thm_2Egcd_2Egcd__ind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2507 (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]. 7.43/7.44 2508 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V1b_2E0)))) & (all V2d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))))))) # label(thm_2Egcd_2EGCD__IS__GREATEST__COMMON__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2509 (all V0m_2E0 all V1n_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),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,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),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,V1n_2E0)))))) # label(thm_2Egcd_2EBINARY__GCD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2510 (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]. 7.43/7.44 2511 (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]. 7.43/7.44 2512 (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_2Egcd_2Egcd_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Egcd_2Egcd_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2513 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V0a_2E0)) # label(thm_2Egcd_2EGCD__0R) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2514 (all V0m_2E0 all V1n_2E0 all V2k_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_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2k_2E0))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Egcd_2EGCD__CANCEL__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2515 (all V0p_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Egcd_2EP__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2516 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2517 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Egcd_2EIS__GCD__REF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2518 (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]. 7.43/7.44 2519 (all V0p_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_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)))))))))) # label(thm_2Egcd_2EPRIME__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2520 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2EIS__GCD__MINUS__R) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2521 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2522 (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]. 7.43/7.44 2523 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Egcd_2EIS__GCD__0L) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2524 (all F0_2E0 ((all V0m_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)),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) -> (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_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,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))))) # label(thm_2Egcd_2Elcm__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2525 (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]. 7.43/7.44 2526 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2527 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2528 (all V0a_2E0 s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Egcd_2EGCD__REF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2529 (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]. 7.43/7.44 2530 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Egcd_2EGCD__SYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2531 (all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0))) = s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) # label(thm_2Egcd_2EIS__GCD__SYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2532 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2EIS__GCD__MINUS__L) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2533 (all V0n_2E0 all 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_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> (all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,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,V2p_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | -p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Egcd_2ELCM__LEAST) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2534 (all V0a_2E0 all V1b_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))))) # label(thm_2Egcd_2EGCD__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2535 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2536 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Egcd_2EGCD__ADD__L__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2537 (all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0)))) # label(thm_2Egcd_2EGCD__ADD__L__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2538 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Egcd_2EIS__GCD__0R) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2539 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0))) = s(tyop_2Enum_2Enum,V0a_2E0)) # label(thm_2Egcd_2EGCD__0L) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2540 (all V0p_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_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_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Egcd_2EPRIME__GCD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2541 (all V0n_2E0 all 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,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_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Egcd_2ELCM__LE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2542 (all V0a_2E0 all V1b_2E0 all V2c_2E0 all V3d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V3d_2E0)))) -> s(tyop_2Enum_2Enum,V2c_2E0) = s(tyop_2Enum_2Enum,V3d_2E0))) # label(thm_2Egcd_2EIS__GCD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2543 (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]. 7.43/7.44 2544 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2545 (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]. 7.43/7.44 2546 (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]. 7.43/7.44 2547 (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_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,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,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_2Egcd_2Egcd_2E2(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))))))))) # label(thm_2Egcd_2EGCD__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2548 (all V0y_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Enum_2Enum,V0y_2E0)) # label(thm_2Egcd_2Egcd__def__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2549 (all V3y_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_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_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_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_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_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_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_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,V3y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_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_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_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_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_2E0)))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2550 (all V7y_2E0 all V8x_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_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_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_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,V7y_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_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)))))))))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2551 (all V9y_2E0 all V10x_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10x_2E0)))))))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2552 (all V5y_2E0 all V6x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_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,V6x_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_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,V5y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_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,V6x_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_2E0)))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2553 (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2554 (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2555 (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]. 7.43/7.44 2556 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Egcd_2Elcm_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Egcd_2Elcm_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2557 (all V0x_2E0 (s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_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,V0x_2E0))) & s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(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,V0x_2E0))) # label(thm_2Egcd_2ELCM__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2558 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2559 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V1m_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> (exists V2p_2E0 exists V3q_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_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))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V3q_2E0))) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))))) # label(thm_2Egcd_2EFACTOR__OUT__GCD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2560 (all F0_2E0 ((all V0a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0a_2E0))) -> (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V0a_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Egcd_2EGCD__EFFICIENTLY) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2561 (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]. 7.43/7.44 2562 (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]. 7.43/7.44 2563 (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]. 7.43/7.44 2564 (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]. 7.43/7.44 2565 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Egcd_2EGCD__ADD__R) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2566 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2c_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & (all V3d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2c_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2Eis__gcd__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2567 (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]. 7.43/7.44 2568 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2569 (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]. 7.43/7.44 2570 (all X0_2E0 all X1_2E0 all 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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Egcd_2Eis__gcd_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Egcd_2Eis__gcd_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2571 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> (exists V2rt_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2rt_2E0),s(tyop_2Enum_2Enum,V0r_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_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2rt_2E0))),s(tyop_2Enum_2Enum,V0r_2E0)))))))))) # label(thm_2Elogroot_2EROOT__exists) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2572 (all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V2y_2E0))))))))) # label(thm_2Elogroot_2EROOT__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2573 (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]. 7.43/7.44 2574 (all F4_2E0 all F3_2E0 all F2_2E0 all F1_2E0 all F0_2E0 ((all V4e_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Enum_2Enum,V4e_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V4e_2E0))) -> ((all V2d_2E0 all V3c_2E0 all V4e_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Enum_2Enum,V4e_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2d_2E0),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,V3c_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V4e_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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,V4e_2E0)))) -> ((all V2d_2E0 all V3c_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,V2d_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,V3c_2E0)))) -> ((all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,V2d_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),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,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))))) -> ((all V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),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,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))) -> (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))))))) # label(thm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2575 (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]. 7.43/7.44 2576 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.43/7.44 2577 (all V0b_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,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)))) -> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2y_2E0))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))))))) # label(thm_2Elogroot_2ELOG__add__digit) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2578 (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]. 7.43/7.44 2579 (all V0a_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,V0a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_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))))))))) # label(thm_2Elogroot_2ELOG__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2580 (all V0e_2E0 all V1a_2E0 all V2b_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,V0e_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))) # label(thm_2Elogroot_2ELT__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2581 (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]. 7.43/7.44 2582 (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]. 7.43/7.44 2583 (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_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Elogroot_2ELOG_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))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Elogroot_2ELOG_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))))))))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Elogroot_2ELOG__MOD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2584 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2585 (all V0a_2E0 all V1b_2E0 all V2c_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,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) -> s(tyop_2Enum_2Enum,V2c_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0))))))))) # label(thm_2Elogroot_2ELOG__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2586 (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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2587 (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]. 7.43/7.44 2588 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(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_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2589 (all X0_2E0 all X1_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)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2590 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Elogroot_2EROOT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elogroot_2EROOT_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2591 (all V0n_2E0 all V1a_2E0 all V2b_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_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,V1a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))))))) # label(thm_2Elogroot_2ELOG__ADD1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2592 (all V0a_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_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,V0a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) # label(thm_2Elogroot_2ELOG__DIV) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2593 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2594 (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]. 7.43/7.44 2595 (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]. 7.43/7.44 2596 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_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))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_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))),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_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_2Elogroot_2ESQRTd__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2597 (all V0a_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2p_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_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0)))))))) -> s(tyop_2Enum_2Enum,V2p_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Elogroot_2ELOG__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2598 (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]. 7.43/7.44 2599 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Elogroot_2Enumeral__root2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2600 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2601 (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]. 7.43/7.44 2602 (all F2_2E0 all F1_2E0 all F0_2E0 ((all V2d_2E0 (s(tyop_2Enum_2Enum,V2d_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))))) -> ((all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,V2d_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(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,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))),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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(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,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))),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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2d_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 V1p_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))) -> (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))))) # label(thm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2603 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2604 (all V0r_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0r_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_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0r_2E0)))))) -> s(tyop_2Enum_2Enum,V2p_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Elogroot_2EROOT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2605 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_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,V1a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))) # label(thm_2Elogroot_2ELOG__EXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2606 (all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0r_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V2y_2E0))))) # label(thm_2Elogroot_2EROOT__DIV) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2607 (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]. 7.43/7.44 2608 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2609 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT0_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2610 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2611 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0r_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_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V0r_2E0)))))))) # label(thm_2Elogroot_2EROOT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.44 2612 (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]. 7.43/7.44 2613 (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]. 7.43/7.44 2614 (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]. 7.43/7.44 2615 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2616 (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]. 7.43/7.45 2617 (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]. 7.43/7.45 2618 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2619 (all V0m_2E0 all V1n_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,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Elogroot_2ELOG__RWT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2620 (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_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elogroot_2ELOG_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2621 (all F4_2E0 all F3_2E0 all F2_2E0 all F1_2E0 all F0_2E0 ((all V4e_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V4e_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Enum_2Enum,V4e_2E0)))))) -> ((all V2d_2E0 all V3c_2E0 all V4e_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,V4e_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Enum_2Enum,V4e_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2d_2E0),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,V3c_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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,V4e_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 V2d_2E0 all V3c_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,V3c_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F3_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3c_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))))) -> ((all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,V2d_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),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,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))))) -> ((all V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),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,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))) -> (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))))) # label(thm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2622 (all V0a_2E0 all V1n_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,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1n_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_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))))))) # label(thm_2Elogroot_2ELOG) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2623 (exists V0f_2E0 all V1a_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,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,V1a_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(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)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_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)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Elogroot_2ELOG__exists) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2624 (all V0b_2E0 all V1x_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)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))))) # label(thm_2Elogroot_2ELOG__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2625 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2626 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2627 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2628 (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]. 7.43/7.45 2629 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2630 (all V0a_2E0 all V1b_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) # label(thm_2Elogroot_2EEXP__LT__ISO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2631 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_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,V0a_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))))) # label(thm_2Elogroot_2ELOG__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2632 (all V0a_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_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,V0a_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2y_2E0))))))))) # label(thm_2Elogroot_2ELOG__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2633 (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]. 7.43/7.45 2634 (all V0a_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,V0a_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_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Elogroot_2ELOG__BASE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2635 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT3_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT3_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2636 (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]. 7.43/7.45 2637 (all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V2c_2E0)))) # label(thm_2Elogroot_2EEXP__MUL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2638 (all V0e_2E0 all V1a_2E0 all V2b_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,V0e_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) # label(thm_2Elogroot_2ELE__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2639 (all F0_2E0 ((all V1n_2E0 all V0r_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,V0r_2E0))))),s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,V2x_2E0)))) -> (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0r_2E0))),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,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0r_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) & s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elogroot_2EROOT__COMPUTE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2640 (all F2_2E0 all F1_2E0 all F0_2E0 ((all V2d_2E0 (s(tyop_2Enum_2Enum,V2d_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))))) -> ((all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,V2d_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V2d_2E0))),s(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,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))),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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(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,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V2d_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 V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))) -> (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2641 (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]. 7.43/7.45 2642 (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]. 7.43/7.45 2643 (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]. 7.43/7.45 2644 (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]. 7.43/7.45 2645 (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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2646 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2647 (all V0n_2E0 (s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_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,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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(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_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_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_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,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elogroot_2Enumeral__sqrt) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2648 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ESQRTd_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2ESQRTd_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2649 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2650 (all V0a_2E0 all V1b_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) # label(thm_2Elogroot_2EEXP__LE__ISO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2651 (all V0a_2E0 all V1x_2E0 all V2r_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,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))))) # label(thm_2Elogroot_2ELOG__ROOT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2652 (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]. 7.43/7.45 2653 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enmap_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enmap_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2654 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) <-> s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Enumpair_2Etri__11) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2655 (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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2656 (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]. 7.43/7.45 2657 (all A_27a all V0P_2E0 ((all V1n_2E0 all V2f_2E0 all V3l_2E0 ((s(tyop_2Enum_2Enum,V3l_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(A_27a,V1n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3l_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(A_27a,V1n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0))),s(tyop_2Enum_2Enum,V3l_2E0)))))) -> (all V4v_2E0 all V5v1_2E0 all V6v2_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(A_27a,V4v_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V5v1_2E0))),s(tyop_2Enum_2Enum,V6v2_2E0))))))) # label(thm_2Enumpair_2Enlistrec__ind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2658 (all V0t_2E0 all V1nlist_2E0 all V2h_2E0 (s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1nlist_2E0))) = s(tyop_2Enum_2Enum,V1nlist_2E0) & s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2h_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,V0t_2E0),s(tyop_2Enum_2Enum,V1nlist_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))),s(tyop_2Enum_2Enum,V1nlist_2E0))))) # label(thm_2Enumpair_2Enapp__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2659 (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]. 7.43/7.45 2660 (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]. 7.43/7.45 2661 (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]. 7.43/7.45 2662 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumpair_2Enfst__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2663 (all F0_2E0 ((all V0f_2E0 all V1n_2E0 all V2t_2E0 all V3r_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_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,V3r_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2t_2E0))),s(tyop_2Enum_2Enum,V3r_2E0)))) -> (all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlistrec_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))))))) # label(thm_2Enumpair_2Enmap__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2664 (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]. 7.43/7.45 2665 (all V0n_2E0 all V1a_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))))))))) # label(thm_2Enumpair_2ESND__invtri0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2666 (all V0h_2E0 all V1t_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1t_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_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1t_2E0)))) # label(thm_2Enumpair_2Encons__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2667 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Einvtri__le) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2668 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enmap_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enmap_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2669 (all V0n_2E0 all V1a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1a_2E0)))))) # label(thm_2Enumpair_2Einvtri0__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2670 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(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_2Epair_2Eprod(tyop_2Enum_2Enum,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_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2671 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epair_2ESND_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_2ESND_2E0),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]. 7.43/7.45 2672 (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]. 7.43/7.45 2673 (all A_27a all X0_2E0 all X1_2E0 all X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Enumpair_2Enfoldl_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enfoldl_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2674 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Ensnd_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Ensnd_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2675 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2676 (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]. 7.43/7.45 2677 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2678 (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]. 7.43/7.45 2679 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlen_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enlen_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2680 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumpair_2Ensnd__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2681 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Enumpair_2Etri__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2682 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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)))))))))))) # label(thm_2Enumpair_2Etri__def__compute_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2683 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2684 (all V0y_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,V0y_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))) # label(thm_2Enumpair_2Ensnd__npair) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2685 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Enumpair_2Etri__LT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2686 (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]. 7.43/7.45 2687 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Enfst__le) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2688 (all V0n_2E0 all V1a_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_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,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_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_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_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_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_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)))))))))))) # label(thm_2Enumpair_2Einvtri0__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2689 (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]. 7.43/7.45 2690 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(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,V1n_2E0)))) # label(thm_2Enumpair_2Enpair__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2691 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Einvtri__lower) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2692 (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]. 7.43/7.45 2693 (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_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(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))))))))))))) # label(thm_2Enumpair_2Einvtri__upper) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2694 (all V0P_2E0 ((all V1h_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2t_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_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2t_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 V3n_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_2Enumpair_2Enlist__ind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2695 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2696 (all F0_2E0 ((all V2n_2E0 all V3t_2E0 all V4r_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V4r_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3t_2E0))),s(tyop_2Enum_2Enum,V4r_2E0)))) -> (all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enlistrec_2E3(s(tyop_2Enum_2Enum,V1l2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,V0l1_2E0),s(tyop_2Enum_2Enum,V1l2_2E0)))))) # label(thm_2Enumpair_2Enapp__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2697 (all F0_2E0 ((all V0n_2E0 all V1t_2E0 all V2r_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2r_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,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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1t_2E0))),s(tyop_2Enum_2Enum,V2r_2E0)))) -> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlistrec_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlen_2E0))) # label(thm_2Enumpair_2Enlen__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2698 (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]. 7.43/7.45 2699 (all V0y_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0y_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_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0y_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_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0y_2E0))) # label(thm_2Enumpair_2Einvtri__unique) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2700 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Etri__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2701 (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_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(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]. 7.43/7.45 2702 (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]. 7.43/7.45 2703 (all V0P_2E0 ((all V1n_2E0 all V2a_2E0 ((-p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_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),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_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_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_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))))) -> (all V3v_2E0 all V4v1_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,V3v_2E0))),s(tyop_2Enum_2Enum,V4v1_2E0))))))) # label(thm_2Enumpair_2Einvtri0__ind) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2704 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Ensnd__le) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2705 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Enumpair_2Enlistrec_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enlistrec_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2706 (all A_27a all F1_2E0 all F0_2E0 ((all V0f_2E0 all V4n_2E0 all V5t_2E0 all V6r_2E0 all V7a_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,V5t_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V6r_2E0))),s(A_27a,V7a_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6r_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)),V0f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V7a_2E0)))))) -> ((all V3a_2E0 s(A_27a,V3a_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V3a_2E0)))) -> (all V0f_2E0 all V1a_2E0 all V2l_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Enumpair_2Enlistrec_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))),s(tyop_2Enum_2Enum,V2l_2E0))),s(A_27a,V1a_2E0))) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1a_2E0),s(tyop_2Enum_2Enum,V2l_2E0))))))) # label(thm_2Enumpair_2Enfoldl__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2707 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2708 (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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumpair_2Enlistrec_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enlistrec_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enlistrec_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2709 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2710 (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]. 7.43/7.45 2711 (all V0n_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,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) & (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumpair_2Etri__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2712 (all V0t_2E0 all V1h_2E0 all V2f_2E0 (s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Enumpair_2Enmap__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2713 (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_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2714 (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]. 7.43/7.45 2715 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.43/7.45 2716 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | (exists V1h_2E0 exists V2t_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2t_2E0)))))) # label(thm_2Enumpair_2Enlist__cases) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2717 (all V0n_2E0 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,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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)))))))))) # label(thm_2Enumpair_2Etwotri__formula) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2718 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))))))) # label(thm_2Enumpair_2Einvtri__linverse__r) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2719 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Enumpair_2Etri__LT__I) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2720 (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]. 7.43/7.45 2721 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Einvtri_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2722 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Einvtri__linverse) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2723 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlistrec_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumpair_2Enlistrec_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enlistrec_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2724 (all V0n_2E0 exists V1x_2E0 exists V2y_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Enumpair_2Enpair__cases) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2725 (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]. 7.43/7.45 2726 (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]. 7.43/7.45 2727 (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_2Enumpair_2Enapp_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enapp_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2728 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Enumpair_2Etri__LE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2729 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Etri_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Etri_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2730 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumpair_2Einvtri__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2731 (all V0t_2E0 all V1h_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,V0t_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_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Enumpair_2Enlen__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2732 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Enpair) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2733 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Enumpair_2Etri__formula) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2734 (all A_27a all F0_2E0 ((all V1l_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1l_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))))) -> (all V0n_2E0 all V1l_2E0 all V2f_2E0 s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,V1l_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1l_2E0))),s(A_27a,V0n_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1l_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_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1l_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,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1l_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)))))))))))))))))) # label(thm_2Enumpair_2Enlistrec__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2735 (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]. 7.43/7.45 2736 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enfst_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enfst_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2737 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Enumpair_2Etri__le) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2738 (all V0y_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))) # label(thm_2Enumpair_2Enfst__npair) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2739 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Enumpair_2Enpair_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enpair_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2740 (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_2Enumpair_2Encons_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Encons_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2741 (all V0y_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) # label(thm_2Enumpair_2Encons__not__nnil) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2742 (all V0y2_2E0 all V1y1_2E0 all V2x2_2E0 all V3x1_2E0 (s(tyop_2Enum_2Enum,V2x2_2E0) = s(tyop_2Enum_2Enum,V3x1_2E0) & s(tyop_2Enum_2Enum,V1y1_2E0) = s(tyop_2Enum_2Enum,V0y2_2E0) <-> s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V2x2_2E0),s(tyop_2Enum_2Enum,V0y2_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V3x1_2E0),s(tyop_2Enum_2Enum,V1y1_2E0))))) # label(thm_2Enumpair_2Enpair__11) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2743 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Enumpair_2Enlistrec_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Enumpair_2Enlistrec_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enlistrec_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2744 (all A_27a all V0t_2E0 all V1n_2E0 all V2h_2E0 all V3f_2E0 (s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V1n_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,V2h_2E0))),s(tyop_2Enum_2Enum,V0t_2E0))),s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) = s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))))) # label(thm_2Enumpair_2Enlistrec__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2745 (all V0y_2E0 all V1x_2E0 all V2t_2E0 all V3h_2E0 (s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V3h_2E0),s(tyop_2Enum_2Enum,V2t_2E0))) <-> s(tyop_2Enum_2Enum,V3h_2E0) = s(tyop_2Enum_2Enum,V1x_2E0) & s(tyop_2Enum_2Enum,V2t_2E0) = s(tyop_2Enum_2Enum,V0y_2E0))) # label(thm_2Enumpair_2Encons__11) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2746 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2747 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumpair_2Einvtri0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Einvtri0_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2748 (all A_27a all V0t_2E0 all V1h_2E0 all V2f_2E0 all V3a_2E0 (s(A_27a,V3a_2E0) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27a,V3a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27a,V3a_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_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)),V2f_2E0),s(tyop_2Enum_2Enum,V1h_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Enum_2Enum,V0t_2E0))))) # label(thm_2Enumpair_2Enfoldl__thm) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2749 (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]. 7.43/7.45 2750 (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]. 7.43/7.45 2751 (all V0n_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Ebit_2EADD__BITS__SUC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2752 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EBIT__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2753 (all V0b_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__THM3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2754 (all V0h_2E0 all V1l_2E0 all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))),s(tyop_2Enum_2Enum,V3b_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3b_2E0)))) # label(thm_2Ebit_2EBITS__SUM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2755 (all F0_2E0 ((all V3a_2E0 all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_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)),F0_2E0),s(tyop_2Enum_2Enum,V3a_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> (all V0n_2E0 all V1m_2E0 all V2i_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2Enum_2Enum,V3a_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2EEXP_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,V1m_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0))))))))))))) # label(thm_2Ebit_2EBIT__SHIFT__THM5) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2756 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOG2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOG2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2757 (all V0h_2E0 all V1l_2E0 all V2x_2E0 all V3y_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) # label(thm_2Ebit_2ESLICE__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2758 (all V0n_2E0 all V1h_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Ebit_2ESLICE__ZERO__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2759 (all V0b_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Ebit_2EBIT__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2760 (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]. 7.43/7.45 2761 (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_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1j_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,V2k_2E0),s(tyop_2Enum_2Enum,V1j_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2EMOD__PLUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.45 2762 (all F0_2E0 all F1_2E0 ((all V0l_2E0 all V1h_2E0 all V3i_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V0l_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0l_2E0))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,V3i_2E0)))))) -> ((all V3i_2E0 all V1h_2E0 all V0l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0l_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,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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,V0l_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> (all V0l_2E0 all V1h_2E0 all V2n_2E0 all V3i_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0l_2E0) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESIGN__EXTEND_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0l_2E0))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0l_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,V0l_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Ebit_2EBIT__SIGN__EXTEND) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2763 (all V0h_2E0 all V1l_2E0 all V2a_2E0 all V3b_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2a_2E0))) <-> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V0h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))))) # label(thm_2Ebit_2EBIT__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2764 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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_2Ebit_2ELOG2__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2765 (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]. 7.43/7.46 2766 (all V0n_2E0 all V1i_2E0 all V2a_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))) # label(thm_2Ebit_2EBIT__SHIFT__THM4) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2767 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),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,c_2Enum_2E0_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_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Ebit_2ENOT__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2768 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))))) # label(thm_2Ebit_2EBITSLT__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2769 (all V3n_2E0 all V4op_2E0 all V5x_2E0 all V6y_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4op_2E0),s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V6y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4op_2E0),s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V6y_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(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)),V4op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V5x_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V6y_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(thm_2Ebit_2EBITWISE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2770 (all V0op_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0op_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) # label(thm_2Ebit_2EBITWISE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2771 (all V0h_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))))) # label(thm_2Ebit_2EBITS__ZERO3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2772 (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]. 7.43/7.46 2773 (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]. 7.43/7.46 2774 (all V0x_2E0 all V1n_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_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,V2a_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))))) # label(thm_2Ebit_2EBIT__REVERSE__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2775 (all X0_2E0 all X1_2E0 all 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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ebit_2EMOD__2EXP__EQ_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EMOD__2EXP__EQ_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2776 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebit_2EBITWISE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Ebit_2EBITWISE_2E4) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2777 (all V0b_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0b_2E0)))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) -> (exists V2i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))))))) # label(thm_2Ebit_2EEXISTS__BIT__LT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2778 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0m_2E0) -> (exists V1p_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1p_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Ebit_2ENOT__ZERO__ADD1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2779 (all V0b_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Ebit_2ESBIT__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2780 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Ebit_2EBITS__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2781 (all V0n_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V1p_2E0))) # label(thm_2Ebit_2ELOG2__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2782 (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]. 7.43/7.46 2783 (all V0x_2E0 all V1n_2E0 all V2f_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))))) # label(thm_2Ebit_2EBIT__MODIFY__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2784 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_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_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_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_2EEXP_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,V1b_2E0))))))) # label(thm_2Ebit_2EDIV__SUB1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2785 (all V0h_2E0 all V1l_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,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0))))))) # label(thm_2Ebit_2EBITS__LT__HIGH) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2786 (all V0h_2E0 all V1h2_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1h2_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h2_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) # label(thm_2Ebit_2EBITS__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2787 (all V0x_2E0 all V1n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIVMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EDIVMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2788 (all V0x_2E0 all V1n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIVMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EDIVMOD__2EXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2789 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0)))))))) # label(thm_2Ebit_2EBIT__TWO__POW) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2790 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(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))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Ebit_2EODD__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2791 (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]. 7.43/7.46 2792 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBITS_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EBITS_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2793 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2794 (all V0n_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & (all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Ebit_2ELEAST__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2795 (all F0_2E0 ((all V0l_2E0 all V2n_2E0 all V1h_2E0 all V3m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0l_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,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1h_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0l_2E0))))),s(tyop_2Enum_2Enum,V3m_2E0))),s(tyop_2Enum_2Enum,V3m_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Enum_2Enum,V0l_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,V3m_2E0)))) -> (all V0l_2E0 all V1h_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Enum_2Enum,V0l_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0l_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESIGN__EXTEND_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Ebit_2ESIGN__EXTEND__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2796 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0a_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_2E0)))))) # label(thm_2Ebit_2ELESS__EQ__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2797 (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_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2798 (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]. 7.43/7.46 2799 (all V0n_2E0 all V1h_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2l_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1h_2E0)))))))))))) # label(thm_2Ebit_2EMOD__2EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2800 (all V0n_2E0 all V1a_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))),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_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))))) # label(thm_2Ebit_2EMOD__2EXP__MAX__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2801 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Ebit_2EBITS__SUC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2802 (all V0b_2E0 all V1m_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,V1m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Ebit_2ESBIT__DIV) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2803 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,V1n_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))))))) # label(thm_2Ebit_2EDIV__MULT__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2804 (all V0h_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2EBITS__ZERO2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2805 (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,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Ebit_2EBITS__LOG2__ZERO__ID) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2806 (all V0h_2E0 all V1m_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) # label(thm_2Ebit_2ESLICE__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2807 (all V0h_2E0 all V1l_2E0 all V2x_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V3n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V2x_2E0)))) # label(thm_2Ebit_2EBITS__DIV__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2808 (all F0_2E0 ((all V0n_2E0 all V1i_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)),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(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)),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2ELOWEST__SET__BIT__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2809 (all V0b_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Ebit_2ESBIT__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2810 (all V0i_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0i_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EBIT__IMP__GE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2811 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2812 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V1y_2E0))))))))) # label(thm_2Ebit_2ELOG2__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2813 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_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_2EDIV_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))))) # label(thm_2Ebit_2EDIV__GT0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2814 (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]. 7.43/7.46 2815 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2ESLICE__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2816 (all V0y_2E0 all V1x_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__LEM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2817 (all V0n_2E0 all V1h_2E0 all V2l_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1h_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V3a_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))))) # label(thm_2Ebit_2EBIT__OF__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2818 (all V0n_2E0 all V1a_2E0 (s(tyop_2Enum_2Enum,V1a_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))),s(tyop_2Enum_2Enum,V1a_2E0)))))) # label(thm_2Ebit_2EMOD__ZERO__GT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2819 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebit_2EBIT_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)),c_2Ebit_2EBIT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2EBIT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2820 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0)))))) # label(thm_2Ebit_2EDIV__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2821 (all V0h_2E0 all V1l_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,c_2Earithmetic_2EEXP_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,V1l_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2EBITS__LT__LOW) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2822 (all V0m_2E0 all V1n_2E0 (s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Ebit_2EADD__BIT0) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2823 (all V0x_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_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)),V2op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EBITWISE__NOT__COR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2824 (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]. 7.43/7.46 2825 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2826 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2827 (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_2Ebit_2EMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2828 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))))) # label(thm_2Ebit_2ESLICELT__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2829 (all V0n_2E0 all V1a_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_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) <-> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2ENOT__BITS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2830 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOWEST__SET__BIT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOWEST__SET__BIT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2831 (all V0h_2E0 all V1m_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2l_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) # label(thm_2Ebit_2EBIT__COMP__THM3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2832 (all V0n_2E0 all V1i_2E0 all V2a_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))) & s(tyop_2Enum_2Enum,V1i_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) | -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))),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,V1i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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_2Ebit_2EBIT__COMPLEMENT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2833 (all V0b_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) # label(thm_2Ebit_2EBITV__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2834 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0)))))))) # label(thm_2Ebit_2EBITS__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2835 (all V0x_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_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)),V2op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V4b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0))))))) # label(thm_2Ebit_2EBITWISE__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2836 (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]. 7.43/7.46 2837 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0)))))) # label(thm_2Ebit_2ETIMES__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2838 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0)))))) # label(thm_2Ebit_2EDIV__MULT__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2839 (all V0i_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0i_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2ENOT__BIT__GT__LOG2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2840 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Ebit_2EBITS__SUC__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2841 (all V0h_2E0 all V1a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,V1a_2E0))) # label(thm_2Ebit_2EBITS__ZEROL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2842 (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 V1x_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_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,V0n_2E0))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_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,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_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))))))))))) # label(thm_2Ebit_2EMOD__ADD__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2843 (all V0i_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0i_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2ENOT__BIT__GT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2844 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2845 (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_2Ebit_2EBIT__REVERSE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBIT__REVERSE_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2846 (all V0h_2E0 all V1m_27_2E0 all V2m_2E0 all V3l_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0h_2E0)))) & s(tyop_2Enum_2Enum,V1m_27_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m_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_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1m_27_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))) # label(thm_2Ebit_2ESLICE__COMP__RWT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2847 (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 V1x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_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))))))) = s(tyop_2Enum_2Enum,V0n_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_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,V0n_2E0))))))) # label(thm_2Ebit_2EMOD__PLUS__1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2848 (all V0a_2E0 all V1b_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0a_2E0))))))) # label(thm_2Ebit_2EEXP__SUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2849 (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_2EEXP_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_2Ebit_2EZERO__LT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2850 (all V0h_2E0 all V1l_2E0 all V2a_2E0 all V3b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0))))),s(tyop_2Enum_2Enum,V3b_2E0))))))) # label(thm_2Ebit_2EBITS__SUM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2851 (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]. 7.43/7.46 2852 (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]. 7.43/7.46 2853 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2854 (all V0h1_2E0 all V1l1_2E0 all V2h2_2E0 all V3l2_2E0 all V4n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0h1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h1_2E0),s(tyop_2Enum_2Enum,V1l1_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(thm_2Ebit_2EBITS__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2855 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2856 (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]. 7.43/7.46 2857 (all V0l_2E0 all V1h_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2ESLICE__ZERO2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2858 (all V0h_2E0 all V1l_2E0 all V2x_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))) # label(thm_2Ebit_2EBIT__OF__BITS__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2859 (all V0n_2E0 all V1a_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2ENOT__BIT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2860 (all V0x_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_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)),V2op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V4b_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_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EBITWISE__COR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2861 (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]. 7.43/7.46 2862 (all V0a_2E0 all V1b_2E0 (s(tyop_2Enum_2Enum,V1b_2E0) != s(tyop_2Enum_2Enum,V0a_2E0) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_2E0)))))))) # label(thm_2Ebit_2EBIT__B__NEQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2863 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Ebit_2ETIMES__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ETIMES__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2864 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0)))))) # label(thm_2Ebit_2EMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2865 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Earithmetic_2EEXP_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_2Ebit_2EONE__LE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2866 (all V0h_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))))) # label(thm_2Ebit_2EBITS__SUM3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2867 (all V0b_2E0 all V1h_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__THM4) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2868 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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_2Ebit_2ETWOEXP__NOT__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2869 (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_2Ebit_2EMOD__2EXP__MAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP__MAX_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2870 (all V0i_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0i_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))))))) # label(thm_2Ebit_2ENOT__BIT__GT__BITWISE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2871 (all V0a_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))))) # label(thm_2Ebit_2ELESS__MULT__MONO2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2872 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.43/7.46 2873 (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]. 7.43/7.46 2874 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1n_2E0)))))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0x_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2ELT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2875 (all V0n_2E0 all V1op_2E0 all V2a_2E0 all V3b_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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_2Ebit_2EBITWISE__LT__2EXP) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2876 (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_2B_2E2(s(tyop_2Enum_2Enum,V1j_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))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2EMOD__PLUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2877 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2EBIT__LOG2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2878 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2879 (all V0a_2E0 all V1b_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,c_2Earithmetic_2EEXP_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,V1b_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0a_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) & s(tyop_2Enum_2Enum,V2n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> (exists V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))))) # label(thm_2Ebit_2EEXISTS__BIT__IN__RANGE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2880 (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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2ESIGN__EXTEND_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESIGN__EXTEND_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2ESIGN__EXTEND_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2881 (all V0n_2E0 all V1a_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2s_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2s_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2s_2E0))))))))) # label(thm_2Ebit_2EBIT__SHIFT__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2882 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_2E0)))))))) # label(thm_2Ebit_2ETWOEXP__MONO2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2883 (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]. 7.43/7.46 2884 (all V0n_2E0 all V1k_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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_2Ebit_2EMOD__2EXP__LT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2885 (all V0n_2E0 all V1m_2E0 ((all V2i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Ebit_2EBITS__ZERO5) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2886 (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]. 7.43/7.46 2887 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Ebit_2EBIT__REVERSE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2888 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),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,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Ebit_2EBIT__REVERSE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2889 (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]. 7.43/7.46 2890 (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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2891 (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]. 7.43/7.46 2892 (all V0n_2E0 all V1h_2E0 all V2l_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2l_2E0)))))) # label(thm_2Ebit_2ESLICE__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2893 (all V0n_2E0 all V1a_2E0 all V2s_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2s_2E0)))))))) # label(thm_2Ebit_2EBIT__SHIFT__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2894 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Ebit_2EBITS__LEQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2895 (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_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2ELEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2896 (all V0b_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0b_2E0))))))) # label(thm_2Ebit_2EBIT__B) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2897 (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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2898 (all V0f_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2EBIT__MODIFY__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2899 (all V2n_2E0 all V3f_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) # label(thm_2Ebit_2EBIT__MODIFY__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2900 (all V0wl_2E0 all V1op_2E0 all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0wl_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0wl_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0wl_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0wl_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3b_2E0)))))) # label(thm_2Ebit_2EBITWISE__BITS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2901 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),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,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Ebit_2ENOT__MOD2__LEM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2902 (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]. 7.43/7.46 2903 (all V0n_2E0 all V1i_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EBIT__DIV2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2904 (all V0n_2E0 all V1op_2E0 all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2a_2E0),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,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V3b_2E0),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,c_2Ebit_2ESBIT_2E2(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)),V1op_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V2a_2E0))))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3b_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Ebit_2EBITWISE__EVAL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2905 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) <-> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) # label(thm_2Ebit_2EBIT__SLICE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2906 (all V0n_2E0 all V1m_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1m_2E0)))))))) # label(thm_2Ebit_2EDIV__LT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2907 (all V0n_2E0 all V1a_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2s_2E0)))))))))) # label(thm_2Ebit_2EBIT__SHIFT__THM3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2908 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Ebit_2EBITS__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2909 (all V2y_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V2y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,V2y_2E0))))))) # label(thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2910 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0x_2E0))),s(tyop_2Enum_2Enum,V1y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V1y_2E0)))))))) # label(thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2911 (all V0b_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_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_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Ebit_2EBIT__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2912 (all V0h_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))))) # label(thm_2Ebit_2EBITS__MUL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2913 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(thm_2Ebit_2EMOD__LEQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2914 (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_2Ebit_2EBITV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBITV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2915 (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_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESBIT_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ESBIT_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2916 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))))))) # label(thm_2Ebit_2EBITSLT__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2917 (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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2ESLICE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2ESLICE_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2918 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V0a_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)))))) # label(thm_2Ebit_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2919 (all V0n_2E0 all V1a_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_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_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2ENOT__BITS2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2920 (all V0h1_2E0 all V1l1_2E0 all V2h2_2E0 all V3l2_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,V0h1_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h1_2E0),s(tyop_2Enum_2Enum,V1l1_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) # label(thm_2Ebit_2EBITS__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.46 2921 (all F0_2E0 all F1_2E0 ((all V0n_2E0 all V1a_2E0 all V2b_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2b_2E0)))) <-> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))))) -> ((all F0_2E0 all V0n_2E0 all V1a_2E0 all V2b_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2b_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2b_2E0)))))) -> (all V0n_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2b_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_2Enum_2Enum,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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))))) # label(thm_2Ebit_2EADD__BIT__SUC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2922 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Ebit_2EBITS__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2923 (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]. 7.43/7.47 2924 (all V0b_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1n_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_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EBIT__EXP__SUB1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2925 (all V0n_2E0 all V1k_2E0 s(tyop_2Enum_2Enum,V1k_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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_2Ebit_2ETWOEXP__DIVISION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2926 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) # label(thm_2Ebit_2EMOD__2EXP__EQ__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2927 (all F0_2E0 ((all V3x_2E0 all V4y_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)),F0_2E0),s(tyop_2Emin_2Ebool,V3x_2E0))),s(tyop_2Emin_2Ebool,V4y_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V3x_2E0)))) -> (all V0n_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Enum_2ESUC_2E1(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))))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Ebit_2EBITWISE__ONE__COMP__LEM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2928 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = 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_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2ELOG_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2929 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),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,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,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EDIV__MULT__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2930 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2931 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2932 (all V0h_2E0 all V1l_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V0h_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1l_2E0))))))))) # label(thm_2Ebit_2EBITS__ZERO4) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2933 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_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)),c_2Ebit_2EBIT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBIT_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2934 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2935 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V1b_2E0)))))))) # label(thm_2Ebit_2ETWOEXP__MONO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2936 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBIT__MODIFY_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EBIT__MODIFY_2E3) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2937 (all V0b_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,V0b_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2938 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Ebit_2ESLICE__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2939 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Ebit_2EDIV__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EDIV__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2940 (all V0n_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Ebit_2EBITV__def) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2941 (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]. 7.43/7.47 2942 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIVMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EDIVMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EDIVMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2943 (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]. 7.43/7.47 2944 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Ebit_2EBITS__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2945 (all A_27a all A_27b all V0f_2E0 all V1t_2E0 all V2sp_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2sp_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__COMPL__INTER) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2946 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2947 (all A_27a all F0_2E0 ((all V0set_2E0 all V1s_2E0 s(tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0)))))) -> (all V0set_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0)))))) # label(thm_2Epred__set_2EPOW__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2948 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINSERT_2E3(s(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINSERT_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2949 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2950 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2e_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2e_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2951 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & (exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__BERNSTEIN__AUTO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2952 (all A_27a all F0_2E0 ((all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V1x_2E0)))) -> (all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__ID) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2953 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EIMAGE__SURJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2954 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),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(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2955 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EPSUBSET__INSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2956 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2957 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) # label(thm_2Epred__set_2EUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2958 (all A_27a all F0_2E0 ((all V0x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) # label(thm_2Epred__set_2EGSPEC__T) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2959 (all A_27a all V0f_2E0 all V1n_2E0 all V2d_2E0 ((all V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(tyop_2Enum_2Enum,V3n_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)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(tyop_2Enum_2Enum,V1n_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)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))))))))) # label(thm_2Epred__set_2ESUBSET__ADD) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2960 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSE__SET) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2961 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(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_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2962 (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]. 7.43/7.47 2963 (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)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2964 (all A_27a all V0P_2E0 ((all V1x_2E0 ((all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))))))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0)))))))) # label(thm_2Epred__set_2EFINITE__COMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2965 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1f_2E0 exists V2b_2E0 all V3e_2E0 ((exists V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) & s(A_27a,V3e_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__WEAK__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2966 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Epred__set_2ELINV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Epred__set_2ELINV_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ELINV_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2967 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> (all V2f_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__INJ__o) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2968 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1c_2E0 exists V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1c_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EFINITE__BIJ__COUNT__EQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2969 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2EIMAGE__I) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2970 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 s(A_27b,V1b_2E0) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27b,V1b_2E0)))) # label(thm_2Epred__set_2EITSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2971 (all A_27a all V0s_2E0 ((exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EBIJ__NUM__COUNTABLE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2972 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))))) # label(thm_2Epred__set_2ESING__UNION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2973 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Einj__countable) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2974 (all A_27a all X0_2E0 all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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]. 7.43/7.47 2975 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_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_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2976 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2977 (all A_27a 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(A_27c,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_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2978 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (exists V3f_27_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2Einj__surj) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2979 (all A_27a all V0r_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) # label(thm_2Epred__set_2EDIFF__INTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2980 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EFINITE__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2981 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 all V2f_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EFUNSET__THM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2982 (all A_27a all F0_2E0 ((all V0f_2E0 all V2e_2E0 all V3acc_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0)))) -> (all V0f_2E0 all V1s_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2ESUM__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2983 (all A_27a all X0_2E0 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_2Epred__set_2EPOW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPOW_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2984 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EUNIV__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2985 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2986 (all A_27a all V0x_2E0 all V1sos_2E0 ((exists V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__applied) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2987 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(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),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(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),V0s_2E0))))))) # label(thm_2Epred__set_2EBIGUNION__partition) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2988 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Epred__set_2ESUM__SET__SING) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2989 (all V0e_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2EMAX__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2990 (all A_27a all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSED) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2991 (all A_27a all F0_2E0 ((all V0s_2E0 all V1n_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_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EINFINITE__EXPLICIT__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2992 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2993 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2994 (all A_27a all V0p_2E0 all V1q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0)))))) # label(thm_2Epred__set_2ECOMPL__SPLITS) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2995 (all A_27a all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Epred__set_2EBIGINTER__INTER) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2996 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_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_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> s(A_27a,V1y_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),V2s_2E0)))))) # label(thm_2Epred__set_2EIN__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2997 (all A_27a all V0s_2E0 all V1P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2998 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Enum_2Enum,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_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 2999 (all A_27a all V0x_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Epred__set_2ECHOICE__SING) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3000 (all A_27a all V0x_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EDELETE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3001 (all A_27a all A_27b all V0t_2E0 all V1s_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),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EINJ__INR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3002 (all A_27a all V0P_2E0 ((s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0) | s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) & (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2EBIGUNION__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3003 (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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EBIGUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3004 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2n_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__upper__bound) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3005 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Epred__set_2EFINITE__PSUBSET__INFINITE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3006 (all A_27a all V0R_2E0 all V1s_2E0 all V2x_2E0 all 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_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Epred__set_2EREL__RESTRICT_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),V1s_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))))) # label(thm_2Epred__set_2EREL__RESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3007 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) <-> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Epred__set_2EINSERT__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3008 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3009 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EINTER__OVER__UNION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3010 (all A_27a all V0P_2E0 all V1s_2E0 ((all V3t_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_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 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),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_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_2Epred__set_2EFORALL__IN__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3011 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V1y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V1y_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2ESUBSET__K) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3012 (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),c_2Epred__set_2EDFUNSET_2E2(s(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_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,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(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EDFUNSET_2E0),s(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)))) # label(arityeq2_2Ec_2Epred__set_2EDFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3013 (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]. 7.43/7.47 3014 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2u_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))))) # label(thm_2Epred__set_2EIMAGE__SUBSET__gen) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3015 (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_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_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_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_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3016 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,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)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3017 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 all V2s_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),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)),V1f_2E0),s(A_27b,V3y_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_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Epred__set_2EIN__BIGINTER__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3018 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3019 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMAX_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3020 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),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_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3021 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ESUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3022 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2ESUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3023 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3024 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),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(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3025 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__INTER) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3026 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EDISJOINT__DELETE__SYM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3027 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) & (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V4h_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2EBIJ__INJ__SURJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3028 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EABS__DIFF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EABS__DIFF_2E2) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3029 (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]. 7.43/7.47 3030 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3031 (all A_27a all F0_2E0 ((all V0x_2E0 all V1y_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)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0)))) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) -> (all V0x_2E0 all V1y_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1y_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27a,V1y_2E0)))))) # label(thm_2Epred__set_2EDELETE__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3032 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_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),V1s_2E0)))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Epred__set_2ESUM__IMAGE__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3033 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDIFF_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),V0s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDIFF__applied) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3034 (all F1_2E0 all F0_2E0 ((all V1p_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1p_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)),F1_2E0),s(tyop_2Enum_2Enum,V1p_2E0)))) -> ((all V0n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) -> (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) # label(thm_2Epred__set_2Ecount__EQN) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3035 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Epred__set_2ELINV_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EBIJ__LINV__BIJ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3036 (all A_27a all F2_2E0 all F0_2E0 all F1_2E0 ((all V0P_2E0 all V2x_2E0 all 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,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(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) -> ((all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),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))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) -> ((all V0P_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) -> (all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))))))) # label(thm_2Epred__set_2EGSPEC__OR) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3037 (all A_27a all V0s_2E0 all 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),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EDELETE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3038 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2ECOMPL__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3039 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3040 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4x_2E0))) <-> s(A_27a,V5y_2E0) = s(A_27a,V4x_2E0)))))) # label(thm_2Epred__set_2EINJ__IFF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3041 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EGSPEC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EGSPEC_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3042 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__SING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3043 (all A_27a all A_27b all V0t_2E0 all V1s_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),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0t_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EINJ__INL) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3044 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V2p_2E0 all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) -> ((all V0P_2E0 all V1Q_2E0 all V2p_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))),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(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),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)))) -> (all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))))))) # label(thm_2Epred__set_2ECROSS__DEF) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3045 (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2ESUM__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.47 3046 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2Eis__measure__maximal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2Eis__measure__maximal_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3047 (all A_27a all V0e_2E0 all V1s1_2E0 all V2s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__INSERT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3048 (all A_27a all A_27b all F0_2E0 ((all V1s_2E0 all V3y_2E0 all V0f_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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,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),V1s_2E0)))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,V3y_2E0))) -> (all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) & (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(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(A_27b,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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))))))))) # label(thm_2Epred__set_2EBIJ__ALT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3049 (all A_27a all V0x_2E0 all V1y_2E0 (-p(s(tyop_2Emin_2Ebool,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0)))))) # label(thm_2Epred__set_2EK__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3050 (all A_27a all V0s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EFINITE__REST__EQ) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3051 (all A_27a ((exists V0f_2E0 ((exists V3y_2E0 all V4x_2E0 s(A_27a,V3y_2E0) != s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0)))) & (all V1x_2E0 all V2y_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V1x_2E0))) -> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2EINFINITE__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3052 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(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(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3053 (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]. 7.43/7.48 3054 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3055 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Eschroeder__close_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2Eschroeder__close_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2Eschroeder__close_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3056 (all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) & (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) & (all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EMAX__SET__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3057 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V3P_2E0 all V4x_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4x_2E0)))))) -> (all V0f_2E0 all V1y_2E0 all V2x_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V1y_2E0)))) & s(A_27b,V2x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1y_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0)))))))))))) # label(thm_2Epred__set_2EIN__GSPEC) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3058 (all A_27a all V0s_2E0 all V1t_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),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__ALT) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3059 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3060 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__EMPTY__SING) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3061 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EEMPTY__UNION) # label(axiom) # label(non_clause). [assumption]. 7.43/7.48 3062 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EREST__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3063 (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]. 7.53/7.48 3064 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2EPROD__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPROD__IMAGE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3065 (all A_27a all V0X_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))))) <-> (all V2Y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3066 (all A_27a all V0n_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) & (all V3e1_2E0 all V4e2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0)))))) & (all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0)))) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ECARD__BIGUNION__SAME__SIZED__SETS) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3067 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3068 (all A_27a all V0s_2E0 all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EDIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3069 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__EMPTY__REFL) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3070 (all A_27a all A_27b all X0_2E0 all X1_2E0 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_27b,tyop_2Esum_2Esum(A_27a,A_27b)),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_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3071 (all A_27a all V0s_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2Ecompl__insert) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3072 (all A_27a all V0s_2E0 ((exists 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),V0s_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3073 (all A_27a all F0_2E0 ((all V0x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EGSPEC__F) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3074 (all A_27a all V0s_2E0 all V1e_2E0 all V2s2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0)))) # label(thm_2Epred__set_2EDELETE__SUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3075 (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]. 7.53/7.48 3076 (all A_27a all V0x_2E0 all 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_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ECOMPONENT) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3077 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2EPROD__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EPROD__IMAGE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPROD__IMAGE_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3078 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3079 (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),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,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_27b,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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EFUNSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3080 (all A_27a all A_27b all X0_2E0 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(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3081 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EDISJOINT__INSERT_27) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3082 (all A_27a all F0_2E0 ((all V0e_2E0 all V2ps_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2ps_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E1(s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2ps_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2ps_2E0)))) -> (all V0e_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EPOW__EQNS) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3083 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))))) # label(thm_2Epred__set_2ECARD__CROSS) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3084 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2s_2E0 all V3f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) -> s(A_27b,V0y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_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),V2s_2E0)))))) # label(thm_2Epred__set_2ELINV__OPT__THM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3085 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> (all V1f_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & (all V3q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3q_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2p_2E0))))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2p_2E0))))))))) # label(thm_2Epred__set_2ESUM__SAME__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3086 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNION_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))),c_2Epred__set_2EUNION_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_2Ec_2Epred__set_2EUNION_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3087 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2Einter__countable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3088 (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_2Epred__set_2ESING_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESING_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3089 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3090 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3091 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) & (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__BIGUNION__EQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3092 (all A_27a all F0_2E0 ((all V0sp_2E0 all V3u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0)))) -> (all V0sp_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0) & (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0)))))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))))))))) # label(thm_2Epred__set_2EDIFF__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3093 (all V0s_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & (all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1x_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__LEM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3094 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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_2E_2B_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_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) # label(thm_2Epred__set_2Epair__to__num__formula) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3095 (all A_27a s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ESING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3096 (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]. 7.53/7.48 3097 (all A_27a all V0x_2E0 all V1s_2E0 all V2m_2E0 all V3e_2E0 all V4y_2E0 (p(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),V2m_2E0),s(A_27a,V3e_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_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),V1s_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V4y_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V4y_2E0))))) # label(thm_2Epred__set_2Eis__measure__maximal__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3098 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2f_27_2E0 all V3s_27_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),V3s_27_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),V2f_27_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EIMAGE__CONG) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3099 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EEMPTY__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3100 (all A_27a all V0x_2E0 all V1y_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_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) <-> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0))) # label(thm_2Epred__set_2EIN__SING) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3101 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__IFF__EMPTY__REST) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3102 (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]. 7.53/7.48 3103 (all A_27a all V0s_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EDELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3104 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3105 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(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_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3106 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1y_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EDFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1y_2E0)))))) # label(thm_2Epred__set_2EFUNSET__DFUNSET) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3107 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 all V3s0_2E0 all V4t0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4t0_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4t0_2E0)))))) # label(thm_2Epred__set_2EINJ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3108 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & (all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))))))) & (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EMAX__SET__DEF) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3109 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0))) # label(thm_2Epred__set_2ESET__EQ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3110 (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2ECOUNT__SUC) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3111 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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_27b,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EIN__PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3112 (all A_27a all V0s_2E0 all V1x_2E0 all V2x_27_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_27_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))))) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EIN__DELETE__EQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3113 (all A_27a all A_27b all F0_2E0 ((all V2P_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0))),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(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)),V2P_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))))) -> (all V0y_2E0 all V1x_2E0 all V2P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_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)),V2P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V0y_2E0)))))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3114 (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),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,V2y_2E0))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) -> (all V3s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))))) # label(thm_2Epred__set_2EIMAGE__11__INFINITE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3115 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,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_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3116 (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_2Epred__set_2Epair__to__num_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Epair__to__num_2E1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3117 (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]. 7.53/7.48 3118 (all A_27a all F0_2E0 ((all V0s_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0)))) -> (all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E1(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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2Eenumerate__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3119 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EEQUAL__SING) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3120 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3121 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3122 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3123 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__SUBSET__LE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3124 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__SING) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3125 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2ESUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3126 (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)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ECOMPL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECOMPL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3127 (all A_27a all F1_2E0 all F0_2E0 ((all V0R_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),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))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_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,V4y_2E0)))) -> ((all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(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,V1x_2E0))),s(A_27a,V2y_2E0)))))) -> (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)),c_2Erelation_2Einv_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,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V1x_2E0))))))))) -> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V3x_2E0)))))))))))))) # label(thm_2Epred__set_2EKoenigsLemma__WF) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3128 (all A_27a all X0_2E0 s(A_27a,c_2Epred__set_2ECHOICE_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_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3129 (all A_27a all V0x_2E0 all 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),V1s_2E0)))) & s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EIN__REST) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3130 (all A_27a all A_27b all X0_2E0 all 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))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(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]. 7.53/7.48 3131 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3132 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EDIFF__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3133 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) | s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EFINITE__CROSS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3134 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2c_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2c_2E0)))))) # label(thm_2Epred__set_2EFUNSET__INTER) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3135 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_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_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Epred__set_2EFINITE__DIFF__down) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3136 (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(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3137 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3138 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EDISJOINT__UNION__BOTH) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3139 (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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))))))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2Ecount__add1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3140 (all A_27a all V0f_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_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) & (all V1e_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1e_2E0))))))))))) # label(thm_2Epred__set_2EPROD__IMAGE__THM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3141 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,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)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3142 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPHP) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3143 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3144 (all A_27a all V0s2_2E0 all V1s1_2E0 all V2f2_2E0 all V3f1_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_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),V0s2_2E0)))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f1_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f2_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))) # label(thm_2Epred__set_2ESUM__IMAGE__CONG) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3145 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_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(tyop_2Emin_2Efun(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(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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EFUNSET_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_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3146 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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))) -> s(A_27a,V5y_2E0) = s(A_27a,V4x_2E0)))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINJ__DEF) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3147 (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]. 7.53/7.48 3148 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> (exists V3g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> s(A_27b,V4y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(A_27b,V4y_2E0))))))))))) # label(thm_2Epred__set_2ESURJ__INJ__INV) # label(axiom) # label(non_clause). [assumption]. 7.53/7.48 3149 (all A_27a all F0_2E0 ((all V1P_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(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)))))) -> (all V0y_2E0 all V1P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V0y_2E0)))))) # label(thm_2Epred__set_2EIN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3150 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3151 (all A_27a all V0R_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_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_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Epartition__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3152 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3153 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epred__set_2Enum__to__pair_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Enum__to__pair_2E1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3154 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_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_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Epred__set_2Echooser_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Echooser_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3155 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__REST) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3156 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> (all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3e_2E0)))))))))))) # label(thm_2Epred__set_2EINJ__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3157 (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_2Epred__set_2ESUM__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESUM__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3158 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3159 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2EINTER__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3160 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) # label(thm_2Epred__set_2EFINITE__BIJ__CARD) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3161 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EDISJOINT__SYM) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3162 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EPREIMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3163 (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_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_2Epred__set_2ECROSS_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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3164 (all A_27a all V0s_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EINSERT__SING__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3165 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Ecountable__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3166 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EFINITE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.48 3167 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_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_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3168 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V1x_2E0))))))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))))) # label(thm_2Epred__set_2EGSPEC__F__COND) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3169 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2s_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) | -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0)))))))))) # label(thm_2Epred__set_2EBIJ__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3170 (all A_27a all A_27b all V0f_2E0 all V1M_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1M_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1M_2E0)))))) # label(thm_2Epred__set_2EIMAGE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3171 (all A_27a all F1_2E0 all F0_2E0 ((all V2y_2E0 all V0x_2E0 all V1s_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V2y_2E0) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V2y_2E0))),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> ((all V0x_2E0 all V1s_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2y_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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V2y_2E0))),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> (all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2EINSERT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3172 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3173 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists 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),V0s_2E0)))) -> (exists V3n_2E0 s(A_27a,V2x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))) # label(thm_2Epred__set_2ECOUNTABLE__ALT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3174 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__INTER) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3175 (all A_27a all V0s_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),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3176 (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]. 7.54/7.49 3177 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3178 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EINJ__CARD__IMAGE__EQ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3179 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3180 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ESURJ__IMP__INJ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3181 (all X0_2E0 all X1_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)),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_2Ebool_2ELET_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3182 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3183 (all A_27a all V0s1_2E0 all V1s2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3184 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EPREIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EPREIMAGE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3185 (all A_27a all F3_2E0 all F2_2E0 all F1_2E0 all F0_2E0 ((all V4y_2E0 all V1s_2E0 all V0R_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)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(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)),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_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(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_2Ebool)))),F3_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V3x_2E0)))))) -> ((all V1s_2E0 all V0R_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4y_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)),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_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(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_2Ebool)))),F3_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V3x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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,V4y_2E0)))) -> ((all V1s_2E0 all V2t_2E0 all V0R_2E0 (p(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_2Ebool),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_2Ebool),tyop_2Emin_2Efun(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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (exists V3x_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V3x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) -> ((all V1s_2E0 all V0R_2E0 all V2t_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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_2Ebool),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_2Ebool),tyop_2Emin_2Efun(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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Ebool),tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Ebool),V2t_2E0)))) -> (all V0R_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_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_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(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_2Ebool),tyop_2Epair_2Eprod(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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))))))) # label(thm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3186 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | (exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2Ecountable__surj) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3187 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EEMPTY__NOT__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3188 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3189 (all A_27a all V0s_2E0 ((exists V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3190 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ESUBSET__REFL) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3191 (all A_27a all V0x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_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)))))) # label(thm_2Epred__set_2ECARD__SING) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3192 (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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3193 (all A_27a all A_27b (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2EINFINITE__PAIR__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3194 (all A_27a all A_27b 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_27b,A_27a),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(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),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_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3195 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EPREIMAGE__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3196 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),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(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2x_2E0)))) -> (all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3197 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3198 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINSERT__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3199 (all A_27a all V0x_2E0 all 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_2Epred__set_2ECOMPL_2E1(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),V1s_2E0)))))) # label(thm_2Epred__set_2EIN__COMPL) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3200 (all A_27a all A_27b all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> (all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Epred__set_2EBIJ__IMP__11) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3201 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_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))),c_2Epred__set_2EDIFF_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_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3202 (all A_27a all V0s_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))) # label(thm_2Epred__set_2EPSUBSET__SING) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3203 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Epred__set_2EUNIV__FUNSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3204 (all A_27a (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists 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),V0s_2E0))))))))) # label(thm_2Epred__set_2ENOT__IN__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3205 (all A_27a all V0x_2E0 all V1f_2E0 all V2s_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_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> (exists V3n_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_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3206 (all A_27a all V0s_2E0 all V1t_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),V1t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EIN__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3207 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3208 (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_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3209 (all A_27a all A_27b all V0t_2E0 all V1s0_2E0 all V2s_2E0 all V3f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s0_2E0)))))))) # label(thm_2Epred__set_2EINJ__BIJ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3210 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2Einfinite__num__inj) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3211 (all A_27a all V0P_2E0 all V1a_2E0 all V2s_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,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))) | (exists 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),V2s_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_2Epred__set_2EEXISTS__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3212 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(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(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3213 (all A_27a all V0P_2E0 all V1B_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3214 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ECROSS__SINGS) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3215 (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(A_27a,tyop_2Emin_2Ebool),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,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3216 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECOUNTABLE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3217 (all A_27a all A_27b all X0_2E0 s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),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)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3218 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3219 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EREST__SING) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3220 (all A_27a all A_27b all V0z_2E0 all V1s_2E0 all V2f_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(A_27b,V3x_2E0))) = s(A_27a,V0z_2E0))) & s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EIMAGE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3221 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 ((all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_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),V1s_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 V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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_2Epred__set_2EFORALL__IN__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3222 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_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,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECARD__POW) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3223 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EEMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3224 (all A_27a all 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_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ENOT__IN__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3225 (all A_27a 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(A_27c,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_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3226 (all A_27a all V0x_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ESUBSET__OF__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3227 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EINTER__UNION__COMPL) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3228 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ENOT__UNIV__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3229 (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_2Epred__set_2Ecount_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecount_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Ecount_2E2) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3230 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3231 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EEMPTY_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3232 (all A_27a all A_27b all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EEMPTY__FUNSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3233 (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]. 7.54/7.49 3234 (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_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3235 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3236 (all A_27a 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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3237 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__THM) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3238 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) # label(thm_2Epred__set_2EDIFF__DIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3239 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) & (exists V4g_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),V1s_2E0)))) -> s(A_27a,V6x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6x_2E0))))))) & (all V7x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_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_27b,A_27a),V4g_2E0),s(A_27b,V7x_2E0))))) = s(A_27b,V7x_2E0))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V5x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4g_2E0),s(A_27b,V5x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EBIJ__IFF__INV) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3240 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) # label(thm_2Epred__set_2ESURJ__CARD) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3241 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3242 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EDISJOINT__SING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3243 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 all V3t_2E0 all V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))))) # label(thm_2Epred__set_2ESURJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3244 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EREST__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3245 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(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),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(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),V0s_2E0)))))))) # label(thm_2Epred__set_2EEMPTY__NOT__IN__partition) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3246 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EDFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_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)),V2Q_2E0),s(A_27a,V3x_2E0)))))))))) # label(thm_2Epred__set_2EIN__DFUNSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3247 (all A_27a all V0m_2E0 all V1s_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),V1s_2E0)))) & (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(A_27a,V3y_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(A_27a,V2x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Epred__set_2Eis__measure__maximal__def) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3248 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),c_2Epred__set_2ELINV__OPT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ELINV__OPT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3249 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3250 (all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__SET__IN__LE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3251 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V2f_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__PERMUTES) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3252 (all A_27a all V0x_2E0 all 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),V1s_2E0)))) -> (all V2t_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3253 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECOUNTABLE__ALT__BIJ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3254 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EUNIV__FUN__TO__BOOL) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3255 (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(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3256 (all A_27a all F1_2E0 all F0_2E0 ((all V0R_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_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,V4y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),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)))))) -> ((all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(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,V1x_2E0))),s(A_27a,V2y_2E0)))))) -> (all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V1x_2E0))))))))) -> (all V3x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V3x_2E0)))))))) -> (exists V5f_2E0 ((all 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)),V0R_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))))))))) & s(A_27a,V3x_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)))))))))))) # label(thm_2Epred__set_2EKoenigsLemma) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3257 (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_2ETC_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_2ETC_2E1(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]. 7.54/7.49 3258 (all A_27a all V0f_2E0 all V1s_2E0 all V2x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EPROD__SET__IMAGE__REDUCTION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3259 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EINFINITE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3260 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3261 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EDISJOINT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3262 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESING__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3263 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))))) # label(thm_2Epred__set_2ECARD__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3264 (all A_27a all A_27b all V0f_2E0 ((all V2s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) & (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2ESURJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3265 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(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),V0s_2E0)))) -> (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(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),V0s_2E0)))))) -> (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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)))))))))) # label(thm_2Epred__set_2Epartition__elements__interrelate) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3266 (all A_27a all V0x_2E0 all 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),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Epred__set_2EINSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3267 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EDIFF__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3268 (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_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3269 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3270 (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]. 7.54/7.49 3271 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3272 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (exists V3N_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3N_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EBIJ__FINITE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3273 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),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_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3274 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))) # label(thm_2Epred__set_2EUNION__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3275 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2ESUBSET__EQ__CARD) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3276 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(thm_2Epred__set_2ECROSS__INSERT__LEFT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3277 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECARD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 7.54/7.49 3278 (all A_27a all V0y_2E0 all V1x_2E0 all V2m_2E0 (s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(A_27a,V0y_2E0)))))) # label(thm_2Epred__set_2Eis__measure__maximal__SING) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3279 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3280 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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_2Epred__set_2EMAX__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMAX__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3281 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2ECOMPL__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3282 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(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_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3283 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2Esubset__countable) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3284 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,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)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3285 (all V0e_2E0 s(tyop_2Enum_2Enum,V0e_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EMIN__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3286 (all V1s_2E0 all V2e1_2E0 all V3e2_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V2e1_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V3e2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V2e1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V3e2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3287 (all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3288 (all A_27a ((all V2s_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))) & (all V0s_2E0 all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2ESUBSET__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3289 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E1(s(A_27a,V0x_2E0))))) # label(thm_2Epred__set_2EUNIV__applied) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3290 (all A_27a all X0_2E0 all 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_2Epred__set_2ESUBSET_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_2Ebool,c_2Epred__set_2ESUBSET_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_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3291 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3292 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Epred__set_2EEMPTY__applied) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3293 (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]. 7.54/7.50 3294 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3295 (all A_27a all V0B_2E0 all V1A_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0)) & (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))))))) # label(thm_2Epred__set_2EINTER__SUBSET__EQN) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3296 (all A_27a all V0s1_2E0 all V1s2_2E0 all V2s3_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s3_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s3_2E0)))))) # label(thm_2Epred__set_2ESUBSET__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3297 (all A_27a all V0s_2E0 all V1x_2E0 ((exists V2t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EDECOMPOSITION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3298 (all A_27a all V0x_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__BIGUNION__I) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3299 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) & s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EFINITE__SURJ__BIJ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3300 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3301 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_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_2Ebool),X1_2E0))) = 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)),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_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2Epartition_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)))) # label(arityeq2_2Ec_2Epred__set_2Epartition_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3302 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2Ein__max__set) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3303 (all V0P_2E0 all V1Q_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) & (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3304 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V2s_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,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V4x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> (exists V3y_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_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Epred__set_2EEXISTS__IN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3305 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EINTER__applied) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3306 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3307 (all A_27a all V0s_2E0 ((exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EENUMERATE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3308 (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]. 7.54/7.50 3309 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECARD__REST) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3310 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EINJ__IMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3311 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3312 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__IFF__CARD1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3313 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EINSERT__UNION__EQ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3314 (all A_27a all V0s_2E0 all V1t_2E0 all V2g_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDIFF__INTER) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3315 (all A_27a all A_27b all V0S_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_2E0)))) -> (all V1t_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2EFINITE__BIJ__CARD__EQ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3316 (all A_27a all V0s_2E0 all V1t_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),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EIN__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3317 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2Ecross__countable) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3318 (all A_27a all V0s_2E0 -(exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Epow__no__surj) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3319 (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]. 7.54/7.50 3320 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) & (exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V4h_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__BERNSTEIN) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3321 (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)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3322 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3323 (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_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3324 (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]. 7.54/7.50 3325 (all A_27a all V0sp_2E0 all V1s_2E0 ((all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0)))))) & s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3326 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3327 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EIMAGE__PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3328 (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_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3329 (all A_27a all A_27b all F0_2E0 ((all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (all V0s_2E0 all V1f_2E0 all V2b_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,V2b_2E0),s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)),V1f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(A_27b,V2b_2E0))))))),s(A_27b,c_2Ebool_2EARB_2E0))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2b_2E0)))))) # label(thm_2Epred__set_2EITSET__def) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3330 (all A_27a ((all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & (all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3331 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EUNION__OVER__INTER) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3332 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) -> (all V1v_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EIN__EQ__UNIV__IMP) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3333 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EIMAGE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3334 (all A_27a all V0x_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V0x_2E0)))) <-> (all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))))) # label(thm_2Epred__set_2EBIGINTER__applied) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3335 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,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(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3336 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) # label(thm_2Epred__set_2ESUBSET__SUBSET__EQ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3337 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Epred__set_2ECARD__INTER__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3338 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Epred__set_2ECROSS__EMPTY__EQN) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3339 (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))),c_2Epred__set_2EINTER_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,c_2Epred__set_2EINTER_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_2Ec_2Epred__set_2EINTER_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3340 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3341 (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_2Ebool),c_2Epred__set_2EUNION_2E2(s(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_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(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_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Ebool))),c_2Epred__set_2EUNION_2E0),s(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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3342 (all A_27a all F0_2E0 ((all V0P_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(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)))))) -> (all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2EGSPEC__ETA) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3343 (all A_27a all V0f_2E0 all V1s_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__IN__LE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3344 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3345 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2y_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)),V0f_2E0),s(A_27a,V3x_2E0)))))))))) # label(thm_2Epred__set_2EIN__BIGUNION__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3346 (all A_27a all V0m_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Epred__set_2EFINITE__is__measure__maximal) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3347 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0)))))) # label(thm_2Epred__set_2EDIFF__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3348 (all A_27a all A_27b (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2Ecountable__Uprod) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3349 (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_2Ebool),app_2E2(s(tyop_2Emin_2Efun(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_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(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_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3350 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EBIJ__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3351 (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(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_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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EFUNSET_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_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFUNSET_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_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EFUNSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3352 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_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_27c,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3353 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 s(A_27a,c_2Epred__set_2ERINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0))) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0)))))) # label(thm_2Epred__set_2ERINV__LO) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3354 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Epred__set_2ERINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V3x_2E0))))) = s(A_27b,V3x_2E0))))) # label(thm_2Epred__set_2ERINV__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3355 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3356 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3357 (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]. 7.54/7.50 3358 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINSERT_2E3(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2ESING__applied) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3359 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3360 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0)))) # label(thm_2Epred__set_2EDIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3361 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))))) # label(thm_2Epred__set_2EFINITE__INTER) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3362 (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]. 7.54/7.50 3363 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EI_2E0)) # label(thm_2Epred__set_2EPREIMAGE__I) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3364 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECHOICE__NOT__IN__REST) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3365 (all A_27a ((all V2s_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) & (all V0s_2E0 all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3366 (all A_27a all V0x_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))))))) # label(thm_2Epred__set_2ECOMPL__INTER) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3367 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ECROSS_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),V2x_2E0)))))) # label(thm_2Epred__set_2ECROSS__applied) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3368 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3369 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Epred__set_2EFUNSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3370 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2ESUBSET__INTER1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3371 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EINSERT__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3372 (all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2EPROD__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3373 (all A_27a all V0s_2E0 ((all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) & (all V2s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> (all V3e_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EFINITE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3374 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_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_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_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_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2Epartition__CARD) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3375 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3376 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3377 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINJ__CARD) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3378 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),V1t_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ENOT__EQUAL__SETS) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3379 (all A_27a all A_27b all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__K) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3380 (all V0s_2E0 ((exists V2n_2E0 ((all V3m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> (exists V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ENUM__SET__WOP) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3381 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3382 (all A_27a all V0s_2E0 all V1t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2EINFINITE__DIFF__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3383 (all A_27a all V0f_2E0 all V1e_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1e_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2ESUM__IMAGE__SING) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3384 (all A_27a all V0f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))))) # label(thm_2Epred__set_2Ecountable__image__nats) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3385 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2EIMAGE__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3386 (all A_27a all A_27b all F0_2E0 ((all V0x_2E0 all V3P_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4y_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0))),s(A_27a,V4y_2E0)))) -> (all V0x_2E0 all V1b_2E0 all V2a_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V2a_2E0)))) & s(A_27b,V1b_2E0) = s(A_27b,V0x_2E0))))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__1) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3387 (all A_27a all V0s2_2E0 all V1s1_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(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_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))))) # label(thm_2Epred__set_2EREL__RESTRICT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3388 (all A_27a all V0s1_2E0 all V1s2_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__DELETE__BOTH) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3389 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EIN__INFINITE__NOT__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3390 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))))) # label(thm_2Epred__set_2EMAX__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3391 (all A_27a all V0x_2E0 all V1P_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_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),V1P_2E0)))) # label(thm_2Epred__set_2EIN__APP) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3392 (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]. 7.54/7.50 3393 (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(A_27a,tyop_2Emin_2Ebool),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,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3394 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EREL__RESTRICT_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(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(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_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_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(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Epred__set_2EREL__RESTRICT_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.54/7.50 3395 (all A_27a all A_27b (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2Ecountable__Usum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3396 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2Eimage__countable) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3397 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__POW) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3398 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = 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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3399 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_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))),c_2Epred__set_2EINTER_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_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3400 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__COMPL) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3401 (all A_27a ((all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & (all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EINTER__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3402 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) # label(thm_2Epred__set_2EIMAGE__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3403 (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]. 7.57/7.50 3404 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_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_2Epred__set_2EIN__COUNT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3405 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3406 (all A_27a all V0R_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_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_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_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_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Epairwise__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3407 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (exists V3g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V5x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(A_27b,V5x_2E0))) = s(A_27b,V5x_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),V1s_2E0)))) -> s(A_27a,V4x_2E0) = s(A_27a,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Epred__set_2EBIJ__INV) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3408 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = 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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2E_2B_2E1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3409 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(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),X2_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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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)))),c_2Ebool_2ECOND_2E0),s(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),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3410 (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]. 7.57/7.50 3411 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3412 (all A_27a all F1_2E0 all F0_2E0 ((all V2x_2E0 all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> p(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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) -> ((all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(A_27a,V2x_2E0)))) -> (all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EUNION__DEF) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3413 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_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_2Enum_2Enum,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_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3414 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> (all V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.57/7.50 3415 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(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_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3416 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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),V1s_2E0)))))) # label(thm_2Epred__set_2EDELETE__NON__ELEMENT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3417 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1y_2E0))),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EDELETE__COMM) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3418 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) # label(thm_2Epred__set_2EINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3419 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Epred__set_2ESPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3420 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))))))) # label(thm_2Epred__set_2EFUNSET__applied) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3421 (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(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3422 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Epred__set_2ESING) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3423 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2s_2E0 all V3t_2E0 ((all V4y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(A_27a,V1x_2E0) = s(A_27a,V4y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))))) # label(thm_2Epred__set_2EINJ__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3424 (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]. 7.57/7.51 3425 (all A_27a all V0s1_2E0 all V1s2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__UNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3426 (all A_27a ((all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)) & (all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3427 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))))))) # label(thm_2Epred__set_2ECARD__UNION__LE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3428 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ECARD__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3429 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(thm_2Epred__set_2EIN__CROSS) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3430 (all A_27b all X0_2E0 all X1_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3431 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 all V2y_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) <-> s(A_27b,app_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,V2y_2E0))))) -> (all V3s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))) # label(thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3432 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3433 (all A_27a (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))))) # label(thm_2Epred__set_2EFINITE__PSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3434 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3435 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3436 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3437 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> (exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2EBIJ__SYM) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3438 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EEMPTY__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3439 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(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_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3440 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3441 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EEQ__SUBSET__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3442 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))) # label(thm_2Epred__set_2EBIJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3443 (all A_27a all F0_2E0 ((all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V1x_2E0)))) -> (all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EBIJ__ID) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3444 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2t_2E0 all V3s_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINJ__EXTEND) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3445 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> (all V2e1_2E0 all V3e2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0P_2E0),s(A_27a,V2e1_2E0))),s(A_27a,V3e2_2E0)))))))) # label(thm_2Epred__set_2Epairwise__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3446 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2Efinite__countable) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3447 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2Enum__to__pair__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3448 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EFINITE__SURJ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3449 (all A_27a all V0X_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))) <-> (all V2Y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))))))) # label(thm_2Epred__set_2EBIGUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3450 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))))) # label(thm_2Epred__set_2EDIFF__SAME__UNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3451 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3452 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_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_2Ebool),V1s_2E0)))) <-> (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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,V3x_2E0))),s(A_27a,V4y_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,V4y_2E0))),s(A_27a,V3x_2E0))))) & (all V5x_2E0 all V6y_2E0 all V7z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0R_2E0),s(A_27a,V6y_2E0))),s(A_27a,V7z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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,V7z_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),V1s_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,V2x_2E0)))))))) # label(thm_2Epred__set_2Eequiv__on__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3453 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ESUBSET__INTER__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3454 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ECOMPL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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),V1s_2E0)))))) # label(thm_2Epred__set_2ECOMPL__applied) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3455 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Epred__set_2ELINV__OPT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EINJ__LINV__OPT__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3456 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EINJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3457 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2ECOMPL__COMPL) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3458 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2s_2E0 all V3t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> (exists V4u_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0)))))))) # label(thm_2Epred__set_2EBIJ__INSERT__IMP) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3459 (all A_27a all F0_2E0 ((all V1P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(A_27a,V2x_2E0)))) -> (all V0x_2E0 all V1P_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Epred__set_2EIN__ABS) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3460 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1e_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V1e_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ESUM__SET__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3461 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))) # label(thm_2Epred__set_2ECARD__DIFF__EQN) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3462 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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)),c_2Eprim__rec_2E_3C_2E0),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]. 7.57/7.51 3463 (all A_27a all V0f_2E0 all V1N_2E0 ((all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1N_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_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)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1N_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))))) # label(thm_2Epred__set_2EBIGUNION__IMAGE__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3464 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(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),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_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3465 (all A_27a all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3466 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3467 (all A_27a all V0g_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3468 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) # label(thm_2Epred__set_2EINSERT__INTER) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3469 (all A_27a all V0e_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E1(s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EPOW__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3470 (all A_27a all V0n_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EEXPLICIT__ENUMERATE__MONO) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3471 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EPREIMAGE__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3472 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EINFINITE__INJ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3473 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 ((all V2s_2E0 all V3b_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) -> p(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(A_27b,V3b_2E0))))))) -> p(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27b,V3b_2E0)))))) -> (all V4v_2E0 all V5v1_2E0 p(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4v_2E0))),s(A_27b,V5v1_2E0))))))) # label(thm_2Epred__set_2EITSET__IND) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3474 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__EQN) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3475 (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUM__SET__SUBSET__LE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3476 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Epred__set_2ERINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Epred__set_2ERINV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ERINV_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3477 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__POW) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3478 (all A_27a all F0_2E0 ((all V0f_2E0 all V2e_2E0 all V3acc_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0)))) -> (all V0f_2E0 all V1s_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)))))))))) # label(thm_2Epred__set_2EPROD__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3479 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__DIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3480 (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]. 7.57/7.51 3481 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V2s_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3y_2E0)))))) <-> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_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(A_27b,A_27a),V1f_2E0),s(A_27b,V4x_2E0)))))))))) # label(thm_2Epred__set_2EFORALL__IN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3482 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3483 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2s_2E0 all V3b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & (all V4x_2E0 all V5y_2E0 all V6z_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,V5y_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,V4x_2E0))),s(A_27b,V6z_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,V4x_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,V5y_2E0))),s(A_27b,V6z_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,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1e_2E0))),s(A_27b,V3b_2E0))))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27b,V3b_2E0))))) # label(thm_2Epred__set_2ECOMMUTING__ITSET__RECURSES) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3484 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3485 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EBIJ__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3486 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDFUNSET_2E3(s(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(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_27b,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(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(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EDFUNSET_2E0),s(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(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EDFUNSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3487 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3488 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> (all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3e_2E0)))))))))))) # label(thm_2Epred__set_2EBIJ__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3489 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3490 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__FINITE__I) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3491 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3492 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3493 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EIMAGE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3494 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3495 (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_2Epred__set_2ECROSS_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_2Epred__set_2ECROSS_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_2Epred__set_2ECROSS_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3496 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EFINITE__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3497 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EIMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3498 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDIFF__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3499 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 all V3t_2E0 all V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))))) # label(thm_2Epred__set_2EBIJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3500 (all A_27a all V0A_2E0 all V1B_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Epred__set_2EUNION__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3501 (all A_27a 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_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3502 (all A_27a all V0X_2E0 all V1Y_2E0 all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Y_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2P_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3503 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2ESUBSET__PSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3504 (all A_27a all V0B_2E0 all V1A_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))) # label(thm_2Epred__set_2EINTER__UNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3505 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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),V1s_2E0)))))) # label(thm_2Epred__set_2EABSORPTION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3506 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EFINITE__UNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3507 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EINSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3508 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(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_2Ebool),X1_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3509 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_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_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Epred__set_2EREL__RESTRICT_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_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__StrongOrder__WF) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3510 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EBIGUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3511 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EFINITE__INJ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3512 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_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_2Ebool),V1s_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_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_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_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EFINITE__WF__noloops) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3513 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 ((exists V2t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EINJ__IMAGE__BIJ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3514 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(thm_2Epred__set_2ECROSS__INSERT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3515 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3516 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) & (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EFINITE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3517 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 ((all V2x_2E0 all V3y_2E0 all V4z_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,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,V3y_2E0))),s(A_27b,V4z_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,V3y_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,V2x_2E0))),s(A_27b,V4z_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V5x_2E0 all V6b_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V5x_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,V5x_2E0))),s(A_27b,V6b_2E0))))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27b,V6b_2E0)))))) # label(thm_2Epred__set_2ECOMMUTING__ITSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3518 (all A_27a all V0x_2E0 all V1s_2E0 (s(A_27a,V0x_2E0) != s(A_27a,c_2Epred__set_2ECHOICE_2E1(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),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EREST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EREST__applied) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3519 (all A_27a all F0_2E0 ((all V0sp_2E0 all V2u_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) -> (all V0sp_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EDIFF__BIGINTER1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3520 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNION_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),V0s_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EUNION__applied) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3521 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDELETE__INTER) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3522 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EI_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0)))) # label(thm_2Epred__set_2EIMAGE__II) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3523 (all A_27a ((all V0s_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V3s_2E0 all V4n_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))))) & (all V1s_2E0 all V2n_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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))))))))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Epred__set_2Echooser__def__compute) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3524 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3525 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3526 (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]. 7.57/7.51 3527 (all A_27a all F1_2E0 all F0_2E0 ((all V0P_2E0 all V1x_2E0 ((exists V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0)))))) -> ((all V0P_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0)))) -> (all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))))))))) # label(thm_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3528 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__INSERT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3529 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0)))) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))))) # label(thm_2Epred__set_2EMIN__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3530 (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]. 7.57/7.51 3531 (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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3532 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3533 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EBIGINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3534 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3535 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EFINITE__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.57/7.51 3536 (all A_27a all A_27b all V0t_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) # label(thm_2Epred__set_2EINJ__CARD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3537 (all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))))))) # label(thm_2Epred__set_2ESUM__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3538 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) & (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2e_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) -> (all V3s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__INDUCT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3539 (all A_27a all X0_2E0 s(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_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3540 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,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(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3541 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3542 (all A_27a all F0_2E0 ((all V0y_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0)))))) -> (all V0y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0)))) # label(thm_2Epred__set_2EGSPEC__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3543 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ECARD__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3544 (all A_27a all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3545 (all V0e_2E0 (s(tyop_2Enum_2Enum,V0e_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) & s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Epred__set_2EMAX__SET__REWRITES) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3546 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3547 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ECARD__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3548 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECHOICE__INSERT__REST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3549 (all A_27a all A_27b all V0x_2E0 all 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),V1s_2E0)))) -> (all V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__IN) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3550 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EFINITE__CROSS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3551 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3552 (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_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_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_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_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),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_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3553 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EINSERT__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3554 (all A_27a all A_27b all V0f_2E0 all V1v_2E0 ((exists V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27b,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2Epred__set_2EGSPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3555 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EPOW__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3556 (all A_27a ((all V3s_2E0 all V4t_2E0 ((all V5s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_27_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3s_2E0)))))))) & (all V0s_2E0 all V1t_2E0 ((all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EDISJOINT__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3557 (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)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EREST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EREST_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3558 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Epred__set_2Epair__to__num__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3559 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ENOT__PSUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3560 (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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Epred__set_2ELINV__OPT_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Epred__set_2ELINV__OPT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ELINV__OPT_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3561 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ECARD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3562 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__INTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3563 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V1x_2E0 all V0f_2E0 all V2y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27b,V1x_2E0) <-> p(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(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,V2y_2E0)))))) -> ((all V1x_2E0 all V0f_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,V2y_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,V2y_2E0)))) -> (all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))))))) -> (all V3s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))))))))) # label(thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3564 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__LEQ__MAX__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3565 (all A_27a all A_27b all A_27c all V0P_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2ECROSS__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3566 (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]. 7.58/7.52 3567 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3568 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3569 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFUNSET_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_2Emin_2Efun(A_27a,A_27b),V2x_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EFUNSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3570 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & (exists V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EPSUBSET__MEMBER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3571 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3572 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = 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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3573 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3574 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3575 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__COMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3576 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3577 (all A_27a ((all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) & s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Epred__set_2ECARD__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3578 (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))),c_2Epred__set_2EDIFF_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,c_2Epred__set_2EDIFF_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_2Ec_2Epred__set_2EDIFF_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3579 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_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))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3580 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2ESND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) # label(thm_2Epred__set_2EGSPEC__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3581 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> (exists 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),V0s_2E0))))))) # label(thm_2Epred__set_2EMEMBER__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3582 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3583 (all A_27a all V0f_2E0 ((all V1m_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) != s(tyop_2Enum_2Enum,V1m_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_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)),V0f_2E0),s(tyop_2Enum_2Enum,V1m_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)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) -> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_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)),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))))))))) # label(thm_2Epred__set_2EDISJOINT__COUNT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3584 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) | (exists V1x_2E0 exists V2t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ESET__CASES) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3585 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESUM__IMAGE_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3586 (all A_27a all V0f_2E0 ((all V1e_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1e_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ESUM__IMAGE__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3587 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3588 (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]. 7.58/7.52 3589 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3590 (all A_27a all F1_2E0 all F0_2E0 ((all V0P_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(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0)))) <-> (all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) -> ((all V0P_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V1x_2E0)))) -> (all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3591 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2ECARD__COUNT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3592 (all A_27a all F1_2E0 all F0_2E0 ((all V2x_2E0 all V0s_2E0 all V1t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) -> ((all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) -> (all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EDIFF__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3593 (all F0_2E0 ((all V0n_2E0 all V1m_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) -> (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Epred__set_2Ecount__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3594 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3595 (all A_27a all A_27b all V0x_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))))) # label(thm_2Epred__set_2ECARD__SING__CROSS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3596 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EUNIV__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3597 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> (all V3x_2E0 all V4y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V4y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,V4y_2E0))))) # label(thm_2Epred__set_2EINJ__LINV__OPT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3598 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V1f_2E0 exists V2b_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EFINITE__BIJ__COUNT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3599 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(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_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3600 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(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(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3601 (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_2Epred__set_2EDELETE_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_2Epred__set_2EDELETE_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_2Epred__set_2EDELETE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3602 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3603 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EINSERT__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3604 (all A_27a all V0set_2E0 all V1e_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0)))) # label(thm_2Epred__set_2EIN__POW) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3605 (all A_27a all A_27b all F0_2E0 ((all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (all V0s_2E0 all V1f_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2b_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,V2b_2E0),s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)),V1f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(A_27b,V2b_2E0))))))))))) # label(thm_2Epred__set_2EITSET__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3606 (all A_27a all A_27b all V0s2_2E0 all V1s1_2E0 all V2f_2E0 ((all V3x_2E0 all V4y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) <-> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0))) -> (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))) # label(thm_2Epred__set_2EIMAGE__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3607 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))))))) # label(thm_2Epred__set_2EIN__FUNSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3608 (all A_27a all V0s_2E0 all V1M_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),V0s_2E0))))) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1M_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1M_2E0),s(A_27a,V4y_2E0)))))))))))) # label(thm_2Epred__set_2ESET__MINIMUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3609 (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]. 7.58/7.52 3610 (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_2Esum_2Esum(A_27b,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(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3611 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2EUNION__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3612 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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_2Epred__set_2EMIN__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMIN__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3613 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))) # label(thm_2Epred__set_2ESUM__IMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3614 (all A_27a all X0_2E0 all 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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2Epairwise_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_2Ebool,c_2Epred__set_2Epairwise_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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Epairwise_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3615 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))))) # label(thm_2Epred__set_2Eunion__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3616 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) # label(thm_2Epred__set_2ESUBSET__UNION__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3617 (all A_27a all V0x_2E0 all V1y_2E0 all V2P_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_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))) & s(A_27a,V0x_2E0) != s(A_27a,V1y_2E0) | s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0))) # label(thm_2Epred__set_2EIN__INSERT__EXPAND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3618 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3619 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(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),V0s_2E0)))) -> (all V2t1_2E0 all V3t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(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),V0s_2E0)))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(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),V0s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0)))))))) # label(thm_2Epred__set_2Epartition__elements__disjoint) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3620 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_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(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_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)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3621 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Enumpair_2Enpair_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enpair_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3622 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3623 (all V0n2_2E0 all V1n1_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1n1_2E0))) <-> s(tyop_2Enum_2Enum,V1n1_2E0) = s(tyop_2Enum_2Enum,V0n2_2E0))) # label(thm_2Epred__set_2ECOUNT__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3624 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))))) # label(thm_2Epred__set_2ECARD__UNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3625 (all A_27a all A_27b all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3626 (all A_27a all A_27b all A_27c all V0s_2E0 all V1t_2E0 all V2u_2E0 ((exists V3f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1t_2E0))))) & (exists V4g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V4g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0))))) -> (exists V5h_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V5h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0))))))) # label(thm_2Epred__set_2EBIJ__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3627 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_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),V1s_2E0)))) & (all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,V2y_2E0) = s(A_27a,V0x_2E0))))) # label(thm_2Epred__set_2EUNIQUE__MEMBER__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3628 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3629 (all A_27a all V0I_2E0 all V1J_2E0 all V2n_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__MIN__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3630 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Epred__set_2Eenumerate_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Eenumerate_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3631 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) # label(thm_2Epred__set_2ESUBSET__INSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3632 (all A_27a all V0P_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> (exists 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),V0P_2E0))))))) # label(thm_2Epred__set_2EINFINITE__INHAB) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3633 (all A_27a ((all V1s_2E0 all V2n_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) & (all V0s_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Epred__set_2Echooser__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3634 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(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_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3635 (all A_27a all V0x_2E0 all V1B_2E0 ((all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_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_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))))))) # label(thm_2Epred__set_2EIN__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3636 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3637 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Epred__set_2EFINITE__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3638 (all A_27a all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ECOUNTABLE__IMAGE__NUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3639 (all A_27a all A_27b all F0_2E0 ((all V0x_2E0 all V3P_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(A_27b,V4y_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0))),s(A_27b,V4y_2E0)))) -> (all V0x_2E0 all V1b_2E0 all V2a_2E0 all V3P_2E0 (s(A_27a,V2a_2E0) = s(A_27a,V0x_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(A_27b,V1b_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0)))))))))))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3640 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EEMPTY__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3641 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__SUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3642 (all A_27a all F0_2E0 ((all V1f_2E0 all V0g_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0))),s(A_27a,V3x_2E0)))) -> (all V0g_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Epred__set_2EABS__DIFF__SUM__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3643 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_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)),V2Q_2E0),s(A_27a,V3x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))) # label(thm_2Epred__set_2EDFUNSET__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3644 (all V0I_2E0 all V1J_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__MAX__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3645 (all A_27a ((all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & (all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2EUNION__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3646 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EDELETE__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3647 (all A_27a all F1_2E0 all F0_2E0 ((all V1x_2E0 all V0y_2E0 (s(A_27a,V0y_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)),F1_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0y_2E0)))))) -> ((all V0y_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0y_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_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)),F1_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0y_2E0)))))) -> (all V0y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0y_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Epred__set_2EGSPEC__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3648 (all A_27a all A_27b all V0f_2E0 all V1v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EGSPEC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V1v_2E0)))) <-> (exists V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27b,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))))) # label(thm_2Epred__set_2EGSPECIFICATION__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3649 (all A_27a all V0n_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EEXPLICIT__ENUMERATE__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3650 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_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_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0)) # label(thm_2Epred__set_2EREL__RESTRICT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3651 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))))))))) # label(thm_2Epred__set_2ELESS__CARD__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3652 (all A_27a all X0_2E0 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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.52 3653 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3654 (all A_27a all A_27b all F0_2E0 ((all V0P_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),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))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,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)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))))) -> (all V0P_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)),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))))) # label(thm_2Epred__set_2EGSPEC__PAIR__ETA) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3655 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EPSUBSET__IRREFL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3656 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3657 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EBIJ__SYM__IMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3658 (all A_27a all V0s_2E0 all 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),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))))) # label(thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3659 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2Einj__image__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3660 (all A_27a s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ECARD__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3661 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Epred__set_2ELINV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ELINV_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3662 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_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))),c_2Epred__set_2EUNION_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_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3663 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) # label(thm_2Epred__set_2ESUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3664 (all A_27a all V0g_2E0 all V1f_2E0 all V2m_2E0 all V3n_2E0 (s(tyop_2Enum_2Enum,V2m_2E0) != s(tyop_2Enum_2Enum,V3n_2E0) & (all V5n_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)),V0g_2E0),s(tyop_2Enum_2Enum,V5n_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_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)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V5n_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)),V1f_2E0),s(tyop_2Enum_2Enum,V5n_2E0)))))) & (all V4n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V1f_2E0),s(tyop_2Enum_2Enum,V4n_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)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_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)),V0g_2E0),s(tyop_2Enum_2Enum,V2m_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)),V0g_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))) # label(thm_2Epred__set_2EDISJOINT__DIFFS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3665 (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_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3666 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Epred__set_2Ecount__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3667 (all A_27a all X0_2E0 all 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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2Eequiv__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_2Ebool,c_2Epred__set_2Eequiv__on_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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Eequiv__on_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3668 (all A_27a all V0s_2E0 ((all 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),V0s_2E0))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) # label(thm_2Epred__set_2EEQ__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3669 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3670 (all A_27a all A_27b all V0y_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V0y_2E0)))) <-> (exists 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,V0y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EIMAGE__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3671 (all A_27a all F2_2E0 all F0_2E0 all F1_2E0 ((all V0P_2E0 all V2x_2E0 all V1Q_2E0 (p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) -> ((all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),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)))) -> ((all V0P_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V3x_2E0)))) -> (all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))))))) # label(thm_2Epred__set_2EGSPEC__AND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3672 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2P0_2E0 all V3Q0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q0_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P0_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2ECROSS__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3673 (all A_27a all F0_2E0 ((all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V1x_2E0)))) -> (all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EINJ__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3674 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) <-> (all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EEXTENSION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3675 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_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_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3676 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 all V3t_2E0 all V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))))) # label(thm_2Epred__set_2EINJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3677 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ECOMPL__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3678 (all A_27a all F0_2E0 ((all V1x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V1x_2E0))) = s(A_27a,V1x_2E0)) -> (all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ESURJ__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3679 (all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ECOUNTABLE__NUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3680 (all A_27a all F0_2E0 ((all V2P_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))) -> (all V0b_2E0 all V1a_2E0 all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27a,V0b_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))))) <-> s(A_27a,V0b_2E0) = s(A_27a,V1a_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1a_2E0)))))))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__same) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3681 (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]. 7.58/7.53 3682 (all A_27a all A_27b all F0_2E0 ((all V0a_2E0 all V3y_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))),F0_2E0),s(A_27a,V0a_2E0))),s(A_27b,V3y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0a_2E0),s(A_27b,V3y_2E0)))) -> (all V0a_2E0 all V1s1_2E0 all V2s2_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_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))),F0_2E0),s(A_27a,V0a_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))))))))) # label(thm_2Epred__set_2ECROSS__EQNS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3683 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_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_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_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_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__partition) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3684 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3685 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,V3x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V3x_2E0))))))))) # label(thm_2Epred__set_2EBIJ__LINV__INV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3686 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EPREIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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_27b,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3687 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)) # label(thm_2Epred__set_2EBIGINTER__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3688 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3689 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3690 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ESUBSET__INTER2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3691 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3692 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3693 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Einfinite__rest) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3694 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_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)),c_2Epred__set_2Ecount_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecount_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3695 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Epred__set_2ECROSS__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3696 (all A_27a all V0t_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2ECOMPL__UNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3697 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDIFF__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3698 (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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3699 (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]. 7.58/7.53 3700 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2Eunion__countable) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3701 (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]. 7.58/7.53 3702 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E1(s(A_27a,X0_2E0))) = 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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EINSERT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3703 (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]. 7.58/7.53 3704 (all A_27a all F1_2E0 all F0_2E0 ((all V2x_2E0 all V0s_2E0 all V1t_2E0 (p(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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) -> ((all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(A_27a,V2x_2E0)))) -> (all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2EINTER__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3705 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Epred__set_2ECOUNTABLE__COUNT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3706 (all A_27a all F0_2E0 ((all V1f_2E0 all V0s_2E0 all V4n_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V4n_2E0)))) -> (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V1f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) & (all V2n_2E0 all V3m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),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,V3m_2E0))) -> s(tyop_2Enum_2Enum,V3m_2E0) = s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Epred__set_2EFINITE__ISO__NUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3707 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2n_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__lower__bound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3708 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_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_2Epred__set_2EPSUBSET_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_2Epred__set_2EPSUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3709 (all A_27a all V0c_2E0 ((exists V1f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0c_2E0)) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0c_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0c_2E0)))))) # label(thm_2Epred__set_2ECOUNTABLE__ENUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3710 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EBIGINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3711 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2Ecross__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3712 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 ((all V2x_2E0 all V3y_2E0 (s(A_27a,V3y_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))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2ECARD__INJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3713 (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)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3714 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__EMPTY__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3715 (all A_27a all V0x_2E0 all 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),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EABSORPTION__RWT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3716 (all A_27a all V0s_2E0 all V1t_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),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EIN__INTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3717 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Epred__set_2EFINITE__COUNT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3718 (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_2Epred__set_2EPROD__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPROD__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3719 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Ensnd_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Ensnd_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3720 (all A_27a all V0g_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V4x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V4x_2E0)))))))) & (exists V3x_2E0 (p(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),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__MONO__LESS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3721 (all A_27a all V0s2_2E0 all V1s1_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0)))) & (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_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,V4y_2E0))),s(A_27a,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)),V2R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))) # label(thm_2Epred__set_2Epairwise__UNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3722 (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,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3723 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3724 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2EDIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3725 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EDIFF__INTER2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3726 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3727 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EUNIV_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3728 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2Eschroeder__close_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Eschroeder__close_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3729 (all A_27a all A_27b all V0y_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) <-> (exists 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,V0y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EIN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3730 (all A_27a all A_27b all V0s2_2E0 all V1s1_2E0 all V2f_2E0 ((all V3x_2E0 all V4y_2E0 (s(A_27a,V4y_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))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4y_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))) # label(thm_2Epred__set_2EDISJOINT__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3731 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EIN__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3732 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 (s(A_27a,V1y_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),V2s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINSERT_2E3(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EINSERT__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3733 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Einfinite__pow__uncountable) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3734 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3735 (all A_27a all V0s_2E0 ((all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Ebigunion__countable) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3736 (all A_27a all F1_2E0 all F0_2E0 ((all V0y_2E0 all V1x_2E0 (s(A_27a,V0y_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)),F1_2E0),s(A_27a,V0y_2E0))),s(A_27a,V1x_2E0)))))) -> ((all V0y_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0y_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_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)),F1_2E0),s(A_27a,V0y_2E0))),s(A_27a,V1x_2E0)))))) -> (all V0y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0y_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Epred__set_2EGSPEC__EQ2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3737 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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),V0s_2E0)))) & s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0))) # label(thm_2Epred__set_2EDELETE__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3738 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_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)),V1Q_2E0),s(A_27a,V3x_2E0)))))))))) # label(thm_2Epred__set_2EDFUNSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3739 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2Ecountable__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3740 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(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(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3741 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_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_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3742 (all A_27a all V0s_2E0 ((exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2Ecountable__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3743 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_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_2Epred__set_2EDISJOINT_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_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3744 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2EUNION__DIFF__2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3745 (all A_27a all A_27b all V0f_2E0 ((all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) & (all V1s_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EBIJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3746 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3747 (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_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),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)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3748 (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_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3749 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EBIGUNION__PAIR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3750 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EPSUBSET__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3751 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1f_2E0 all V2x_2E0 all V3b_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,V3b_2E0))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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)),V1f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))),s(A_27b,V3b_2E0)))))))) # label(thm_2Epred__set_2EITSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3752 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2ESUM__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3753 (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]. 7.58/7.53 3754 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2ECARD__UNION__EQN) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3755 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3756 (all A_27a all A_27b all V0f_2E0 ((all V2s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) & (all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2EINJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3757 (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_2Epred__set_2Ecount_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Epred__set_2ECOUNT__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3758 (all A_27a all V0P_2E0 ((exists V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EFINITE__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3759 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3760 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EINTER__FINITE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3761 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2ESING__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3762 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3763 (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),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3764 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3765 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 ((all V2s_2E0 all V3b_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) -> p(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(A_27b,V3b_2E0))))))) -> p(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27b,V3b_2E0)))))) -> (all V4v_2E0 all V5v1_2E0 p(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_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4v_2E0))),s(A_27b,V5v1_2E0))))))) # label(thm_2Epred__set_2EITSET__ind) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3766 (all X0_2E0 all X1_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)),app_2E2(s(tyop_2Emin_2Efun(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_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3767 (all A_27a all 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_2Epred__set_2EUNIV_2E0))))) # label(thm_2Epred__set_2EIN__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3768 (all A_27a all V0x_2E0 all 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_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))))))) # label(thm_2Epred__set_2EELT__IN__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3769 (all A_27a all A_27b all F0_2E0 ((all V1s_2E0 all V0f_2E0 all V2y_2E0 all V3x_2E0 (s(A_27b,V2y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27b,V2y_2E0))),s(A_27a,V3x_2E0)))))) -> (all V0f_2E0 all V1s_2E0 all V2y_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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),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,A_27b),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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27b,V2y_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))) # label(thm_2Epred__set_2ELINV__OPT__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3770 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_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_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0)))))))) # label(thm_2Epred__set_2ECARD__DELETE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3771 (all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3772 (all A_27a all V0P_2E0 all V1a_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_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),V2s_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 V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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_2Epred__set_2EFORALL__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3773 (all A_27a all V0x_2E0 all V1sos_2E0 ((exists V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))))))) # label(thm_2Epred__set_2EIN__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3774 (all A_27a all A_27b all A_27c all V0f_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1a_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),c_2Epair_2ESND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2b_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__CROSS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3775 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__ALT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3776 (all A_27a all V0f_2E0 all V1s_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eschroeder__close_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0)))) <-> (exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2Eschroeder__close__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.53 3777 (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(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),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_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3778 (all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))))))) # label(thm_2Epred__set_2Epair__to__num__inv_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3779 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Epred__set_2Epair__to__num__inv_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3780 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ESURJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3781 (all A_27a all V0s_2E0 ((exists V1f_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EINFINITE__INJ__NOT__SURJ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3782 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))) = s(A_27a,V3x_2E0))))) # label(thm_2Epred__set_2ELINV__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3783 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) # label(thm_2Epred__set_2EUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3784 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3785 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3786 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0))))) = s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0)))) # label(thm_2Epred__set_2ELINV__LO) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3787 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,V4x_2E0))))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2ESURJ__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3788 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) # label(thm_2Epred__set_2EFINITE__BIJ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3789 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3790 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) -> (all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EPREIMAGE__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3791 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3792 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3793 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3794 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enfst_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enfst_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3795 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EINSERT__COMM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3796 (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]. 7.58/7.54 3797 (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]. 7.58/7.54 3798 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f2_2E0)))))))) # label(thm_2EfixedPoint_2Efnsum__monotone) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3799 (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]. 7.58/7.54 3800 (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]. 7.58/7.54 3801 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0)))) # label(thm_2EfixedPoint_2Efnsum__COMM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3802 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))) & (all V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__greatest__fixedpoint) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3803 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__least__closed) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3804 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(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_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3805 (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]. 7.58/7.54 3806 (all A_27a all A_27b all X0_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)),c_2EfixedPoint_2Eempty_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Eempty_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Eempty_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3807 (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]. 7.58/7.54 3808 (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]. 7.58/7.54 3809 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3810 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2X_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0),s(A_27b,V2X_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_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)),V0f1_2E0),s(A_27b,V2X_2E0))),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)),V1f2_2E0),s(A_27b,V2X_2E0)))))) # label(thm_2EfixedPoint_2Efnsum__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3811 (all A_27a all A_27b p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0))))) # label(thm_2EfixedPoint_2Eempty__monotone) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3812 (all A_27a all X0_2E0 all X1_2E0 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_2Efun(A_27a,tyop_2Emin_2Ebool),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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Efnsum_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3813 (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]. 7.58/7.54 3814 (all A_27a all A_27b all V0x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Eempty_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2EfixedPoint_2Eempty__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3815 (all A_27a all X0_2E0 all 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_2Epred__set_2ESUBSET_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_2Ebool,c_2Epred__set_2ESUBSET_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_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3816 (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]. 7.58/7.54 3817 (all A_27a all V0f_2E0 all 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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__empty) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3818 (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]. 7.58/7.54 3819 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V1g_2E0),s(A_27a,V2X_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(A_27a,V2X_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(A_27a,V2X_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(A_27a,V2X_2E0)))))))) # label(thm_2EfixedPoint_2Efnsum__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3820 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EfixedPoint_2Emonotone_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Emonotone_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3821 (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]. 7.58/7.54 3822 (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]. 7.58/7.54 3823 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__induction) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3824 (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))),c_2Epred__set_2EUNION_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),c_2Epred__set_2EUNION_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_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3825 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3826 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__strong__induction) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3827 (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]. 7.58/7.54 3828 (all A_27a all V0f1_2E0 all V1f2_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0)))))))))) # label(thm_2EfixedPoint_2Elfp__fnsum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3829 (all A_27a all X0_2E0 all 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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EfixedPoint_2Edense_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Edense_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3830 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Elfp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Elfp_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3831 (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]. 7.58/7.54 3832 (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]. 7.58/7.54 3833 (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_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EfixedPoint_2Emonotone_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Emonotone_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3834 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(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(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_2EfixedPoint_2Efnsum_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)))) # label(arityeq3_2Ec_2EfixedPoint_2Efnsum_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3835 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))) # label(thm_2EfixedPoint_2Elfp__fixedpoint) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3836 (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]. 7.58/7.54 3837 (all A_27a all V0f_2E0 all V1X_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) # label(thm_2EfixedPoint_2Eclosed__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3838 (all A_27a all A_27b all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0)))) <-> (all V1X_2E0 all V2Y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(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_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(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_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0)))))))))) # label(thm_2EfixedPoint_2Emonotone__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3839 (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_2EfixedPoint_2Efnsum_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_2EfixedPoint_2Efnsum_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_2EfixedPoint_2Efnsum_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3840 (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]. 7.58/7.54 3841 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2h_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2h_2E0)))) # label(thm_2EfixedPoint_2Efnsum__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3842 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3843 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__strong__coinduction) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3844 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3845 (all A_27a all V0f_2E0 all V1X_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))))) = s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) # label(thm_2EfixedPoint_2Edense__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3846 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27b,X2_2E0))) = 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_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2EfixedPoint_2Efnsum_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3847 (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]. 7.58/7.54 3848 (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]. 7.58/7.54 3849 (all A_27a all F0_2E0 ((all V0f_2E0 all V1X_2E0 s(tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) -> (all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))) # label(thm_2EfixedPoint_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3850 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__coinduction) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3851 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Efnsum_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3852 (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))),c_2Epred__set_2EINTER_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),c_2Epred__set_2EINTER_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_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3853 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))) & (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__greatest__dense) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3854 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Egfp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Egfp_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3855 (all A_27a all F0_2E0 ((all V0f_2E0 all V1X_2E0 s(tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) -> (all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3856 (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]. 7.58/7.54 3857 (all A_27a all V0f_2E0 all V1X_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_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)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__rule__applied) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3858 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eclosed_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Eclosed_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3859 (all A_27a all A_27b all V0f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0))))) # label(thm_2EfixedPoint_2Efnsum__empty) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3860 (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]. 7.58/7.54 3861 (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]. 7.58/7.54 3862 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),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_2Egcdset_2Egcdset_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Egcdset_2Egcdset_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3863 (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]. 7.58/7.54 3864 (all V0s_2E0 all V1g_2E0 ((all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1g_2E0),s(tyop_2Enum_2Enum,V2e_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1g_2E0),s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Egcdset_2Egcdset__greatest) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3865 (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]. 7.58/7.54 3866 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3867 (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]. 7.58/7.54 3868 (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_2Epred__set_2EMIN__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMIN__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3869 (all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3870 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3871 (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]. 7.58/7.54 3872 (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]. 7.58/7.54 3873 (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]. 7.58/7.54 3874 (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]. 7.58/7.54 3875 (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]. 7.58/7.54 3876 (all V0x_2E0 all V1s_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Egcdset_2Egcdset__INSERT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3877 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3878 (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]. 7.58/7.54 3879 (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]. 7.58/7.54 3880 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3881 (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_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Edivides_2Edivides_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3882 (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_2Egcd_2Egcd_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Egcd_2Egcd_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3883 (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]. 7.58/7.54 3884 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3885 (all V0s_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1e_2E0)))))) # label(thm_2Egcdset_2Egcdset__divides) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3886 (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]. 7.58/7.54 3887 (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]. 7.58/7.54 3888 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3889 (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]. 7.58/7.54 3890 (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]. 7.58/7.54 3891 (all F0_2E0 all F1_2E0 all F3_2E0 all F2_2E0 ((all V0s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))) -> ((all V0s_2E0 all V1n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> ((all V0s_2E0 all V2d_2E0 ((all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3e_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V2d_2E0)))))) -> ((all V0s_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2d_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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V2d_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V2d_2E0)))) -> (all V0s_2E0 s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))))))))))))))) # label(thm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3892 (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_2Epred__set_2EMAX__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMAX__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3893 (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]. 7.58/7.54 3894 (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]. 7.58/7.54 3895 (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]. 7.58/7.54 3896 (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]. 7.58/7.54 3897 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_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)),app_2E2(s(tyop_2Emin_2Efun(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_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3898 (all A_27a all V0P1_2E0 all V1P2_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2EEVERY__FILTER__IMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3899 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EEL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3900 (all A_27a all V0x_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_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0)))))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V0x_2E0))) # label(thm_2Elist_2ENOT__NIL__EQ__LENGTH__NOT__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3901 (all A_27a all A_27b all A_27c ((all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (all V1n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V2n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V6n_2E0 all V7h_2E0 all V8t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),V8t_2E0)))))) & (all V3n_2E0 all V4h_2E0 all V5t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_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_2Elist_2Elist(A_27c),V5t_2E0)))))) # label(thm_2Elist_2EDROP__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3902 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3903 (all A_27a all V0y_2E0 all V1x_2E0 all V2l_2E0 (s(A_27a,V1x_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))))) # label(thm_2Elist_2EMEM__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3904 (all A_27a all V0ls_2E0 all V1R_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_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,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2EEVERY2__refl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3905 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3906 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0l_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))))) # label(thm_2Elist_2ELIST__BIND__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3907 (all A_27a all A_27b all V0s_2E0 all V1ls_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V1ls_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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)),V2f_2E0),s(A_27b,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Elist_2EBIGUNION__IMAGE__set__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3908 (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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3909 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3910 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ELENGTH__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3911 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)))),c_2Elist_2EOPT__MMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EOPT__MMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3912 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.54 3913 (all A_27a all A_27b all A_27c all A_27d all F1_2E0 all F0_2E0 ((all V3f2_2E0 all V5p_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,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_27a,A_27d))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27d),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0)))))))) -> ((all V2f1_2E0 all V4p_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0)))) -> (all V0l1_2E0 all V1l2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,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_27a,A_27d))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) & s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))))) # label(thm_2Elist_2EZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3914 (all A_27a all A_27b all V0l_2E0 all V1l_27_2E0 all V2b_2E0 all V3b_27_2E0 all V4f_2E0 all V5f_27_2E0 ((all V6x_2E0 all V7a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_27_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)),V5f_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7a_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)),V4f_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7a_2E0))))) & s(A_27b,V3b_27_2E0) = s(A_27b,V2b_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) -> s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V5f_27_2E0),s(A_27b,V3b_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0))) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4f_2E0),s(A_27b,V2b_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2EFOLDR__CONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3915 (all A_27a all A_27b all A_27c all V0l2_2E0 all V1l1_2E0 all V2f_2E0 all V3R_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) # label(thm_2Elist_2ELIST__REL__MAP1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3916 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3917 (all A_27a all V0ls_2E0 all V1n_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))) # label(thm_2Elist_2EDROP__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3918 (all A_27a all A_27b (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) & (all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EREVERSE__SNOC__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3919 (all A_27a all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> (all V2x_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EEL__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3920 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Elist_2EINDEX__FIND_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EINDEX__FIND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3921 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ESNOC_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3922 (all V0x_2E0 all V1n_2E0 all V2b_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V3a_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Enum_2Enum,V2b_2E0)))))))))) # label(thm_2Elist_2EDISJOINT__GENLIST__PLUS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3923 (all A_27a all V0t2_2E0 all V1t1_2E0 all V2t_2E0 all V3l_2E0 all V4h2_2E0 all V5h1_2E0 all V6h_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))) & s(A_27a,V4h2_2E0) = s(A_27a,V5h1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))))))) # label(thm_2Elist_2EisPREFIX__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3924 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3925 (all A_27a all A_27b all V0l1_2E0 all V1l1_27_2E0 all V2l2_2E0 all V3l2_27_2E0 all V4P_2E0 all V5P_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) & (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_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)),V5P_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_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)),V4P_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))))) & s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) = s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) -> s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))))) # label(thm_2Elist_2EEVERY2__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3926 (all A_27a all V0P_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) != s(tyop_2Elist_2Elist(A_27a),V1l_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,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))))) # label(thm_2Elist_2EFILTER__NEQ__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3927 (all A_27a all V0m2_2E0 all V1m1_2E0 all V2l2_2E0 all V3l1_2E0 all V4e_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) <-> (exists V6l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0m2_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V6l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))) | (exists V5l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1m1_2E0) & s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))))))) # label(thm_2Elist_2EAPPEND__EQ__APPEND__MID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3928 (all A_27a all A_27b all V0xs2_2E0 all V1P_2E0 all V2xs1_2E0 all V3zs_2E0 ((exists V4ys1_2E0 exists V5ys2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0)))) & s(tyop_2Elist_2Elist(A_27b),V3zs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0))),s(tyop_2Elist_2Elist(A_27b),V3zs_2E0)))))) # label(thm_2Elist_2ELIST__REL__SPLIT1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3929 (all A_27a all V0ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) # label(thm_2Elist_2ECARD__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3930 (all A_27a all A_27b all A_27c all A_27d all F1_2E0 all F0_2E0 ((all V4Q_2E0 all V2g_2E0 all V8x_2E0 all V9y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),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_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0))),s(A_27c,V8x_2E0))),s(A_27b,V9y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(A_27c,V8x_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(A_27b,V9y_2E0)))))) -> ((all V5P_2E0 all V3f_2E0 all V6x_2E0 all V7y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(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,A_27a),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,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0))),s(A_27c,V6x_2E0))),s(A_27b,V7y_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)),V5P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(A_27c,V6x_2E0))))),s(A_27b,V7y_2E0)))) -> (all V0l2_2E0 all V1l1_2E0 all V2g_2E0 all V3f_2E0 all V4Q_2E0 all V5P_2E0 (s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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,A_27a),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,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) & s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),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_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))))) # label(thm_2Elist_2EEVERY2__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3931 (all A_27a all A_27b all A_27c all V0l_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0)))) # label(thm_2Elist_2ELIST__BIND__LIST__BIND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3932 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3933 (all A_27a ((all V0acc_2E0 s(tyop_2Elist_2Elist(A_27a),V0acc_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0acc_2E0)))) & (all V1h_2E0 all V2t_2E0 all V3acc_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),V3acc_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V3acc_2E0)))))))) # label(thm_2Elist_2EREV__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3934 (all A_27a -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) # label(thm_2Elist_2EINFINITE__LIST__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3935 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3936 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3937 (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)),c_2Erelation_2ERC_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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))))) # label(thm_2Elist_2ELLEX__total) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3938 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3939 (all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EoHD_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3940 (all A_27a all A_27b all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> (all V2f_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EEL__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3941 (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]. 7.58/7.55 3942 (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_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3943 (all A_27a all V0n_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) # label(thm_2Elist_2ELUPDATE__SAME) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3944 (all A_27b all A_27c all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3945 (all A_27a all F0_2E0 ((all V1P2_2E0 all V0P1_2E0 all V3x_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(A_27a,V3x_2E0))))) <-> p(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0))),s(A_27a,V3x_2E0)))))) -> (all V0P1_2E0 all V1P2_2E0 all V2l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3946 (all A_27a ((all V0f_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0)) & (all V2f_2E0 all V3n_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))) # label(thm_2Elist_2EGENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3947 (all A_27a all V0P_2E0 ((all V1l_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2ESNOC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3948 (all A_27a all F0_2E0 ((all V0l1_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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))))) -> (all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))))) # label(thm_2Elist_2Elength__nub__append) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3949 (all A_27a all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V1t_2E0)) # label(thm_2Elist_2ETL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3950 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3951 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2EFIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFIND_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3952 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3953 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EFILTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3954 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3955 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3956 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))),s(A_27b,V1x_27_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2x_27_27_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(A_27b,V1x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2x_27_27_2E0)))) # label(thm_2Elist_2Elazy__list__case__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3957 (all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3958 (all A_27a all V0l_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> (exists V2h_2E0 exists V3l_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_27_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) & s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_27_2E0))))))) # label(thm_2Elist_2ELENGTH__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3959 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))) & (all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3960 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3961 (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]. 7.58/7.55 3962 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3963 (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]. 7.58/7.55 3964 (all A_27a all F0_2E0 ((all V1l2_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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) -> (all V0l1_2E0 all V1l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) # label(thm_2Elist_2Enub__append) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3965 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3966 (all A_27a all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27d),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3967 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3968 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) & s(tyop_2Elist_2Elist(A_27b),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EZIP__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3969 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3970 (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]. 7.58/7.55 3971 (all A_27a all F0_2E0 ((all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))))))) # label(thm_2Elist_2ESET__TO__LIST__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3972 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2ESWAP__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3973 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3974 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2l_2E0 ((all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(A_27a,V3e_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0),s(A_27a,V3e_2E0))))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) # label(thm_2Elist_2EMAP__EQ__f) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3975 (all A_27a all A_27b all A_27c ((all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (all V1n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)) & (all V2n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V6n_2E0 all V7h_2E0 all V8t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),V8t_2E0)))))) & (all V3n_2E0 all V4h_2E0 all V5t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_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_2Elist_2Elist(A_27c),V5t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),V5t_2E0)))))))) # label(thm_2Elist_2ETAKE__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3976 (all A_27c all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3977 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3978 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),X0_2E0),s(A_27c,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),X0_2E0))),s(A_27c,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3979 (all A_27a all V0x_2E0 all V1ls_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3980 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2ELENGTH__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3981 (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_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3982 (all A_27a all A_27b all A_27c all F0_2E0 ((all V0f1_2E0 all V1f2_2E0 all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(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,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0))),s(A_27a,V4x_2E0))),s(A_27c,V5y_2E0)))) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(A_27c,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(A_27a,V4x_2E0))))) -> (all V0f1_2E0 all V1f2_2E0 all V2l1_2E0 all V3l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27c),V3l2_2E0)))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),V3l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(tyop_2Elist_2Elist(A_27c),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))))))) # label(thm_2Elist_2EMAP__EQ__EVERY2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3983 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3984 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3985 (all V0x_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l_2E0))),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ESNOC_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l_2E0)))))) # label(thm_2Elist_2ESUM__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3986 (all A_27a all A_27b all V0f_2E0 all V1l1_2E0 all V2l2_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2EMAP__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3987 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__LIFT2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ELIST__LIFT2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__LIFT2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3988 (all A_27a all V0ls_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__DROP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3989 (all V0h_2E0 all V1t_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1t_2E0)))))) # label(thm_2Elist_2ESUM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3990 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = 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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2E_2B_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3991 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3992 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3993 (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]. 7.58/7.55 3994 (all A_27a all A_27b (s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) & (all V0x_2E0 all V1l_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0)))))))))))) # label(thm_2Elist_2EUNZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3995 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l1_27_2E0 all V2l2_2E0 all V3l2_27_2E0 all V4a_2E0 all V5a_27_2E0 all V6f_2E0 all V7f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) & s(A_27c,V5a_27_2E0) = s(A_27c,V4a_2E0) & (all V8z_2E0 all V9b_2E0 all V10c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V10c_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V9b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V6f_2E0),s(A_27c,V8z_2E0))),s(A_27a,V9b_2E0))),s(A_27b,V10c_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(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0),s(A_27c,V8z_2E0))),s(A_27a,V9b_2E0))),s(A_27b,V10c_2E0))))) & s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) -> s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V6f_2E0),s(A_27c,V4a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0),s(A_27c,V5a_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))))) # label(thm_2Elist_2EFOLDL2__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3996 (all A_27a all V0l_2E0 all V1e_2E0 ((exists V2pfx_2E0 exists V3sfx_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) # label(thm_2Elist_2EMEM__SPLIT__APPEND__last) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3997 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3998 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 3999 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4000 (all A_27a all V0P_2E0 all V1ls_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) # label(thm_2Elist_2EMEM__dropWhile__IMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4001 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4002 (all A_27a all A_27b all F0_2E0 ((all V0x_2E0 all V1f_2E0 all V2fn1_2E0 ((all V3h_2E0 all V4t_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))))),s(A_27a,V3h_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4t_2E0)))))) & s(A_27b,V0x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool))),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0)))))) -> (all V0x_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool))),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0))))))))) # label(thm_2Elist_2Elist__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4003 (all A_27a ((all V0l1_2E0 all V1l2_2E0 all V2l3_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l3_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) & (all V3l1_2E0 all V4l2_2E0 all V5l3_2E0 (s(tyop_2Elist_2Elist(A_27a),V4l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V5l3_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l3_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))))))) # label(thm_2Elist_2EAPPEND__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4004 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4005 (all A_27f all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ECONS_2E2(s(A_27f,X0_2E0),s(tyop_2Elist_2Elist(A_27f),X1_2E0))) = s(tyop_2Elist_2Elist(A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Elist_2Elist(A_27f)),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Elist_2Elist(A_27f))),c_2Elist_2ECONS_2E0),s(A_27f,X0_2E0))),s(tyop_2Elist_2Elist(A_27f),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4006 (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(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4007 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4008 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,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(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4009 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4010 (all A_27a all V0P_2E0 all V1ls_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2EdropWhile__eq__nil) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4011 (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))),c_2Epred__set_2EUNION_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),c_2Epred__set_2EUNION_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_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4012 (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]. 7.58/7.55 4013 (all A_27a (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & (all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27a),V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1t_2E0)))))))) # label(thm_2Elist_2EFLAT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4014 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4015 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4016 (all A_27a all V0l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ENULL__LENGTH) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4017 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4018 (all A_27a all A_27b all A_27c all V0f_2E0 all V1xs_2E0 all V2ys_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0))),s(tyop_2Elist_2Elist(A_27c),V2ys_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__LIFT2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0),s(tyop_2Elist_2Elist(A_27c),V2ys_2E0)))) # label(thm_2Elist_2ELIST__LIFT2__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.55 4019 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 all V3l3_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) & (all V4n_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,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_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,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0)))))) # label(thm_2Elist_2ELIST__REL__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4020 (all A_27a all V0l1_2E0 all V1l2_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) # label(thm_2Elist_2ELIST__EQ__REWRITE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4021 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELLEX_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4022 (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]. 7.58/7.56 4023 (all A_27a all A_27b all A_27c ((all V0t2_2E0 all V1t1_2E0 all V2h2_2E0 all V3h1_2E0 all V4f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h1_2E0),s(tyop_2Elist_2Elist(A_27b),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V2h2_2E0),s(tyop_2Elist_2Elist(A_27c),V0t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(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)),V4f_2E0),s(A_27b,V3h1_2E0))),s(A_27c,V2h2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),V1t1_2E0),s(tyop_2Elist_2Elist(A_27c),V0t2_2E0)))))) & (all V7v5_2E0 all V8v4_2E0 all V9f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V9f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V8v4_2E0),s(tyop_2Elist_2Elist(A_27b),V7v5_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V5y_2E0 all V6f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V5y_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EMAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4024 (all A_27a all V0l2_2E0 all V1l1_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))))) # label(thm_2Elist_2ETAKE__APPEND2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4025 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4026 (all A_27a all V0L_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Elist_2ELENGTH__LEN) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4027 (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]. 7.58/7.56 4028 (all A_27a all V0x_2E0 all V1ls_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,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))) # label(thm_2Elist_2EMEM__DROP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4029 (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]. 7.58/7.56 4030 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2EEXISTS__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4031 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((all V3a_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0)))))) -> ((all V2SET__TO__LIST_2E0 all V3a_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V2SET__TO__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2EARB_2E0))))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V2SET__TO__LIST_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0)))) -> ((all V0R_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(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)),tyop_2Emin_2Ebool),F0_2E0),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)),V0R_2E0)))) <-> (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> p(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)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(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)),V0R_2E0)))))) -> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ESET__TO__LIST_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Erelation_2EWFREC_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_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(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)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),F1_2E0))))))) # label(thm_2Elist_2ESET__TO__LIST__primitive__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4032 (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(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))) = 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)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4033 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0x_2E0))) # label(thm_2Elist_2EisPREFIX__NILR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4034 (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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) -> (all V3l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))))) # label(thm_2Elist_2EEVERY__MONOTONIC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4035 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2x1_2E0 all V3x2_2E0 ((all V4a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3x2_2E0)))))) -> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0),s(A_27a,V4a_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f1_2E0),s(A_27a,V4a_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V2x1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3x2_2E0) -> s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2x1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0),s(tyop_2Elist_2Elist(A_27a),V3x2_2E0))))) # label(thm_2Elist_2EOPT__MMAP__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4036 (all A_27a all V0l2_2E0 all V1l1_2E0 all V2e_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) | s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) & s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4037 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0)))))) # label(thm_2Elist_2EFLAT__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4038 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EUNIQUE_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EUNIQUE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4039 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2P_2E0 all V3P_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_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_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2EEVERY__CONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4040 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4041 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4042 (all A_27a all A_27b all V0f_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> (s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) # label(thm_2Elist_2EINJ__MAP__EQ__IFF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4043 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4044 (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_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4045 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4046 (all A_27a all V0xs_2E0 all V1n_2E0 all V2m_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))) # label(thm_2Elist_2EoEL__DROP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4047 (all A_27a ((all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) & (all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) & (all V4l1_2E0 all V5l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V5l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V4l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))))) & (all V6l1_2E0 all V7l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V6l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V7l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l1_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_2E0))))))) # label(thm_2Elist_2EAPPEND__EQ__SELF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4048 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4049 (all A_27a all A_27b all A_27c all V0g2_2E0 all V1g1_2E0 all V2f2_2E0 all V3f1_2E0 all V4xs_2E0 all V5ys_2E0 (s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0g2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) <-> s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0g2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))) & s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))))) # label(thm_2Elist_2EMAP__APPEND__MAP__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4050 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27a_29_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4051 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V2h_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) <-> (all V1l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) # label(thm_2Elist_2EFORALL__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4052 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c)))),c_2Elist_2EFOLDL2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27c,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) = s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27c,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4053 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4054 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4055 (all A_27a all V0xs_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0xs_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0xs_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__FLAT__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4056 (all A_27a all V0a1_2E0 all V1a0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0)))) # label(thm_2Elist_2ENOT__CONS__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4057 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) <-> (all V1l_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2ELENGTH__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4058 (all A_27a all A_27b all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(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)),V0R_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))))) # label(thm_2Elist_2ELIST__REL__EVERY__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4059 (all A_27a all V0l1_2E0 all V1x_2E0 all V2l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2EAPPEND__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4060 (all A_27a all V0l2_2E0 all V1l1_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))) # label(thm_2Elist_2ETAKE__APPEND1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4061 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V0l_2E0)))))) # label(thm_2Elist_2EMAP__FLAT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4062 (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]. 7.58/7.56 4063 (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]. 7.58/7.56 4064 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4065 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V1ls_2E0 all V2n_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) -> (all V0f_2E0 all V1ls_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2EGENLIST__EL__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4066 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ELUPDATE_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4067 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2n_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2EEL__APPEND__EQN) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4068 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EREVERSE__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4069 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4070 (all A_27a all V0xs_2E0 all V1n_2E0 all V2y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2y_2E0))) <-> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(A_27a,V2y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))))) # label(thm_2Elist_2EoEL__EQ__EL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4071 (all A_27a all V0n_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Elist_2ENULL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4072 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4073 (all A_27a all V0xs_2E0 all V1x_2E0 all V2n_2E0 all V3m_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_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,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) # label(thm_2Elist_2EoEL__TAKE__E) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4074 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),c_2Elist_2ELUPDATE_2E0),s(A_27b,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4075 (all A_27a all V0x_2E0 all V1l_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> (exists V2l1_2E0 exists V3l2_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0)))))))) # label(thm_2Elist_2EMEM__SPLIT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4076 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4077 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4078 (all A_27a all V0l_2E0 all V1n1_2E0 all V2n2_2E0 ((exists V3l1_2E0 exists V4l2_2E0 (s(tyop_2Enum_2Enum,V2n2_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))) & s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))) & s(tyop_2Enum_2Enum,V1n1_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,V2n2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ELENGTH__EQ__SUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4079 (all A_27a all V0l_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) # label(thm_2Elist_2ELENGTH__NIL__SYM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4080 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4081 (all A_27a all V0l1_2E0 all V1x_2E0 all V2l2_2E0 s(A_27a,V1x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2Eel__append3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4082 (all A_27a all F0_2E0 ((all V1k_2E0 all V0ys_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V1k_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) -> (all V0ys_2E0 all V1k_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V1k_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3y_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3y_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))))) # label(thm_2Elist_2ELUPDATE__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4083 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4084 (all A_27g all A_27h all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27g),X1_2E0),s(tyop_2Elist_2Elist(A_27h),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),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(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27g),X1_2E0))),s(tyop_2Elist_2Elist(A_27h),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4085 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4086 (all A_27a all V0P_2E0 ((all V1s_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> (all V2v_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0))))))) # label(thm_2Elist_2ESET__TO__LIST__IND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4087 (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]. 7.58/7.56 4088 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4089 (all A_27a ((all V1x_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) | s(A_27a,V2h_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))))) & (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))))) # label(thm_2Elist_2EMEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4090 (all A_27a all V0l_2E0 all V1e_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EREVERSE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4091 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4092 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4093 (all A_27a ((all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2Enub__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4094 (all A_27a all V0l1_2E0 all V1l2_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) -> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) # label(thm_2Elist_2ELIST__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4095 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum,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_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4096 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ELENGTH__DROP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4097 (all A_27a all V0ls_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) # label(thm_2Elist_2ELIST__TO__SET__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4098 (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]. 7.58/7.56 4099 (all A_27a all V0l_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,V1m_2E0) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ETAKE__LENGTH__ID__rwt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4100 (all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4101 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> (all V2f_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_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)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))) # label(thm_2Elist_2EMAP2__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4102 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V3s_2E0 all V4x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_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)),V0f_2E0),s(A_27a,V4x_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_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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0))),s(A_27a,V4x_2E0)))) -> (all V0f_2E0 all V1ls_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))))) # label(thm_2Elist_2EFOLDL__UNION__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4103 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4104 (all A_27a all V0P_2E0 all V1ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) # label(thm_2Elist_2ELENGTH__dropWhile__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4105 (all A_27a all A_27b all V0t_2E0 all V1l_2E0 all V2h_2E0 all V3f_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V4x0_2E0 exists V5t0_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x0_2E0),s(tyop_2Elist_2Elist(A_27a),V5t0_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V5t0_2E0))) = s(tyop_2Elist_2Elist(A_27b),V0t_2E0) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4x0_2E0))) = s(A_27b,V2h_2E0))))) # label(thm_2Elist_2EMAP__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4106 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ESINGL__SINGL__APPLY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4107 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) # label(thm_2Elist_2EUNZIP__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4108 (all A_27a all V0n_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Elist_2EGENLIST__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4109 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2l3_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0)))) # label(thm_2Elist_2EAPPEND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4110 (all A_27a all A_27b all F0_2E0 all F1_2E0 ((all V0l_2E0 all V2P_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,V3i_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0))),s(tyop_2Enum_2Enum,V3i_2E0)))))) -> ((all V1k_2E0 all V0l_2E0 all V4i_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Enum_2Enum,V4i_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))))) -> (all V0l_2E0 all V1k_2E0 all V2P_2E0 s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))))))) # label(thm_2Elist_2EsplitAtPki__EQN) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4111 (all A_27a all V0n_2E0 all V1f_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elist_2EGENLIST__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4112 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4113 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Elist_2ESET__TO__LIST__INV) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4114 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4115 (all A_27a all A_27b all A_27c all V0t2_2E0 all V1t1_2E0 all V2t_2E0 all V3h_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V2t_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V2t_2E0))) & s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Elist_2Elist(A_27c),V1t1_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V0t2_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),V1t1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V0t2_2E0))))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EFLAT__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4116 (all A_27a all A_27b all V0xs_2E0 all V1n_2E0 all V2f_2E0 all V3h_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3h_2E0))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V0xs_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3h_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V0xs_2E0)))))) # label(thm_2Elist_2ELUPDATE__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4117 (all A_27a all A_27b all A_27c all V0xs_2E0 all V1gs_2E0 all V2fs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),V2fs_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V1gs_2E0),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),V2fs_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V1gs_2E0))),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0)))) # label(thm_2Elist_2ELIST__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4118 (all A_27a all V0R_2E0 ((exists V1a_2E0 exists 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,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2ELLEX__not__WF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4119 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) # label(thm_2Elist_2EREVERSE__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4120 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4121 (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]. 7.58/7.56 4122 (all A_27a all V0c_2E0 all V1n_2E0 all V2s_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2s_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V2s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__LEFT_2E3(s(A_27a,V0c_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2s_2E0)))) # label(thm_2Elist_2EPAD__LEFT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4123 (all A_27a all A_27b all F0_2E0 ((all V2P_2E0 all V3x_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))))) -> (all V0l1_2E0 all V1l2_2E0 all V2P_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))))) # label(thm_2Elist_2Eevery__zip__snd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4124 (all A_27a all V0ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EFLAT__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4125 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2ETAKE__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4126 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))))),c_2Elist_2ELUPDATE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4127 (all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4128 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4129 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))) # label(thm_2Elist_2ESHORTLEX__LENGTH__LE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4130 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EisPREFIX_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4131 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 ((exists V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2ELLEX__EL__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4132 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4133 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ESNOC_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EMAP__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4134 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4135 (all A_27a all A_27b all V0R_2E0 all V1a0_2E0 all V2a1_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1a0_2E0) | (exists V3h1_2E0 exists V4h2_2E0 exists V5t1_2E0 exists V6t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t1_2E0),s(tyop_2Elist_2Elist(A_27b),V6t2_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,V3h1_2E0))),s(A_27b,V4h2_2E0)))) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h2_2E0),s(tyop_2Elist_2Elist(A_27b),V6t2_2E0))) = s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V5t1_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1a0_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1a0_2E0),s(tyop_2Elist_2Elist(A_27b),V2a1_2E0)))))) # label(thm_2Elist_2ELIST__REL__cases) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 4136 (all A_27a all F0_2E0 ((all V1i_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) != s(tyop_2Enum_2Enum,V1i_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)),F0_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> (all V0xs_2E0 all V1i_2E0 all V2n_2E0 all V3x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3x_2E0),s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))))) # label(thm_2Elist_2EoEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4137 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4138 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4139 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4140 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) # label(thm_2Elist_2EALL__DISTINCT__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4141 (all A_27a all F0_2E0 ((all V1t_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1t_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) -> (all V0h_2E0 all V1t_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(A_27a,V0h_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))) # label(thm_2Elist_2ELAST__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4142 (all A_27a all V0l_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_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_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_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2ELENGTH__TL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4143 (all A_27a all V0l_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2Elast__drop) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4144 (all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4145 (all A_27a all V0P_2E0 all V1x_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_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,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEXISTS__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4146 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4147 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4148 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Elist_2EGENLIST__GENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4149 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4150 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ESHORTLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ESHORTLEX_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4151 (all A_27a all F0_2E0 ((all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V1n_2E0 all V2x_2E0 all V3xs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_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_2Elist_2Elist(A_27a),V3xs_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0)))))))) # label(thm_2Elist_2ETAKE__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4152 (all A_27a all A_27b ((all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) & (all V1h1_2E0 all V2h2_2E0 all V3t_2E0 s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0))))))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0)))))))) # label(thm_2Elist_2ELAST__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4153 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2ESWAP__REVERSE__SYM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4154 (all A_27a all V0l_2E0 p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2Eall__distinct__nub) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4155 (all A_27a all A_27b all V0l1_2E0 all V1l2_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,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) # label(thm_2Elist_2EEL__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4156 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V1ls_2E0 all V2n_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) -> (all V0f_2E0 all V1ls_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))) # label(thm_2Elist_2EIMAGE__EL__count__LENGTH) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4157 (all A_27a all A_27b all V0f_2E0 all V1l_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4158 (all A_27a ((all V0h_2E0 all V1t_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Elist_2ELENGTH) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4159 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4160 (all A_27a ((all V1x_2E0 all V2y_2E0 all V3z_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0)))))))) & (all V0x_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EFRONT__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4161 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,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)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4162 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2EFCONS_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4163 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Enum_2Enum,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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elist_2ELEN_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELEN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4164 (all A_27a all V0P_2E0 ((all V1t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))) -> (all V2h_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2Elist__induction) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4165 (all A_27a all A_27b all V0e_2E0 all V1f_2E0 exists V2fn_2E0 (s(A_27b,V0e_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V3x_2E0 all V4l_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))))) # label(thm_2Elist_2ESNOC__Axiom) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4166 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4167 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2Enub_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2Enub_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4168 (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]. 7.58/7.57 4169 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4170 (all A_27a all V0P_2E0 ((exists V1ls_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) <-> (exists V2n_2E0 exists V3f_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Elist_2Eexists__list__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4171 (all A_27a all A_27b all V0L_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0)))))) # label(thm_2Elist_2EUNZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4172 (all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),c_2Elist_2ELIST__GUARD_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ELIST__GUARD_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__GUARD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4173 (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]. 7.58/7.57 4174 (all V0b_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ELIST__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ECONS_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2ELIST__GUARD__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4175 (all A_27d all A_27e all A_27f all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0))),s(tyop_2Elist_2Elist(A_27e),X2_2E0))) = s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0),s(tyop_2Elist_2Elist(A_27e),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27f_20mono_2EA_27d_20mono_2EA_27e) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4176 (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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2ELLEX__transitive) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4177 (all A_27a all V0P_2E0 all V1L_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,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))))))) # label(thm_2Elist_2EMEM__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4178 (all A_27a all A_27b all F0_2E0 ((all V0P_2E0 all V1f_2E0 all V3x_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),V1f_2E0),s(A_27a,V3x_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(A_27a,V3x_2E0)))) -> (all V0P_2E0 all V1f_2E0 all V2l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEXISTS__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4179 (all A_27a all A_27b all F0_2E0 ((all V3k_2E0 all V4h_2E0 all V6p_2E0 all V7s_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V6p_2E0))))),s(tyop_2Elist_2Elist(A_27b),V7s_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0))),s(A_27b,V4h_2E0))),s(tyop_2Elist_2Elist(A_27b),V6p_2E0))),s(tyop_2Elist_2Elist(A_27b),V7s_2E0)))) -> (all V2P_2E0 all V3k_2E0 all V4h_2E0 all V5t_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(A_27b,V4h_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))),s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0))),s(A_27b,V4h_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))) = s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0)))))) & (all V0P_2E0 all V1k_2E0 s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EsplitAtPki__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4180 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EREV_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EREV_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4181 (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))),c_2Epred__set_2EINTER_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),c_2Epred__set_2EINTER_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_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4182 (all A_27a 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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4183 (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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2ENRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4184 (all A_27a all A_27b ((all V2f_2E0 all V3e_2E0 all V4x_2E0 all V5l_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_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)),V2f_2E0),s(A_27b,V3e_2E0))),s(A_27a,V4x_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(A_27b,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))))) & (all V0f_2E0 all V1e_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V1e_2E0)))) # label(thm_2Elist_2EFOLDL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4185 (all A_27a all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4186 (all A_27a all A_27b all V0xs_2E0 all V1t_2E0 all V2h_2E0 all V3R_2E0 ((exists V4h_27_2E0 exists V5t_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0),s(tyop_2Elist_2Elist(A_27b),V1t_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)),V3R_2E0),s(A_27a,V4h_27_2E0))),s(A_27b,V2h_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V1t_2E0)))))))) # label(thm_2Elist_2ELIST__REL__CONS2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4187 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),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_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4188 (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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2ESHORTLEX__transitive) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4189 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4190 (all A_27a all A_27b all V0f_2E0 all V1l1_2E0 all V2l2_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) # label(thm_2Elist_2EINJ__MAP__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4191 (all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4192 (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 V1ys_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),V1ys_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V1ys_2E0)))))) & (all V2P_2E0 all V3yys_2E0 all V4x_2E0 all V5xs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4x_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0))),s(tyop_2Elist_2Elist(A_27d),V3yys_2E0)))) <-> (exists V6y_2E0 exists V7ys_2E0 (s(tyop_2Elist_2Elist(A_27d),V3yys_2E0) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,V6y_2E0),s(tyop_2Elist_2Elist(A_27d),V7ys_2E0))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27c,V4x_2E0))),s(A_27d,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0),s(tyop_2Elist_2Elist(A_27d),V7ys_2E0)))))))) & (all V8P_2E0 all V9xs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),V8P_2E0),s(tyop_2Elist_2Elist(A_27e),V9xs_2E0),s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ENIL_2E0)))) <-> s(tyop_2Elist_2Elist(A_27e),V9xs_2E0) = s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ENIL_2E0))) & (all V10P_2E0 all V11xxs_2E0 all V12y_2E0 all V13ys_2E0 ((exists V14x_2E0 exists V15xs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(tyop_2Elist_2Elist(A_27g),V15xs_2E0),s(tyop_2Elist_2Elist(A_27h),V13ys_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)),V10P_2E0),s(A_27g,V14x_2E0))),s(A_27h,V12y_2E0)))) & s(tyop_2Elist_2Elist(A_27g),c_2Elist_2ECONS_2E2(s(A_27g,V14x_2E0),s(tyop_2Elist_2Elist(A_27g),V15xs_2E0))) = s(tyop_2Elist_2Elist(A_27g),V11xxs_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(tyop_2Elist_2Elist(A_27g),V11xxs_2E0),s(tyop_2Elist_2Elist(A_27h),c_2Elist_2ECONS_2E2(s(A_27h,V12y_2E0),s(tyop_2Elist_2Elist(A_27h),V13ys_2E0)))))))))) # label(thm_2Elist_2EEVERY2__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4193 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2ELENGTH__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4194 (all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0)))))) # label(thm_2Elist_2ESUM__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4195 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4196 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0)))) # label(thm_2Elist_2ELIST__BIND__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4197 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Elist_2EMAP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4198 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Elist_2EINDEX__FIND_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EINDEX__FIND_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4199 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4200 (all A_27a all V0P_2E0 all V1n_2E0 ((all V2l_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) <-> (all V3l_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))))))) # label(thm_2Elist_2ELENGTH__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4201 (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]. 7.58/7.57 4202 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4203 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4204 (all A_27a all V0ll_2E0 ((exists V1x_2E0 exists V2l_2E0 s(tyop_2Elist_2Elist(A_27a),V0ll_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) | s(tyop_2Elist_2Elist(A_27a),V0ll_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2ESNOC__CASES) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4205 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EoHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4206 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4207 (all A_27a all A_27b all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))) # label(thm_2Elist_2ELIST__REL__EL__EQN) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4208 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_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_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_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4209 (all A_27a all F0_2E0 ((all V0P_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,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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))))) -> (all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EFILTER__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4210 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) # label(thm_2Elist_2EEVERY__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4211 (all A_27a all V0l_2E0 all V1n1_2E0 all V2n2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Enum_2Enum,V2n2_2E0) = s(tyop_2Enum_2Enum,V1n1_2E0)))) # label(thm_2Elist_2EALL__DISTINCT__EL__IMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4212 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = 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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4213 (all A_27a all V0x_2E0 all V1L_2E0 ((exists V2l_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1L_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1L_2E0)))))))))) # label(thm_2Elist_2EMEM__FLAT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4214 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1h_2E0))))) # label(thm_2Elist_2EoHD__thm) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4215 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) # label(thm_2Elist_2EdropWhile__APPEND__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4216 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2EoEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EoEL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4217 (all A_27a all X0_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4218 (all A_27a all V0t2_2E0 all V1t1_2E0 all V2h2_2E0 all V3h1_2E0 all V4R_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (s(A_27a,V2h2_2E0) = s(A_27a,V3h1_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_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)),V4R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V2h2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ELLEX__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4219 (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)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4220 (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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),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)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(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)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4221 (all A_27a all V0m2_2E0 all V1m1_2E0 all V2l2_2E0 all V3l1_2E0 ((exists V5l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V1m1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) | (exists V4l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0m2_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4222 (all A_27a all V0x_2E0 all V1l_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Elist_2ELAST__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4223 (all V0L_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Elist_2ESUM__ACC__SUM__LEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4224 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4225 (all A_27a all A_27b all V0xs2_2E0 all V1P_2E0 all V2xs1_2E0 all V3zs_2E0 ((exists V4ys1_2E0 exists V5ys2_2E0 (s(tyop_2Elist_2Elist(A_27b),V3zs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V3zs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0)))))))) # label(thm_2Elist_2ELIST__REL__SPLIT2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4226 (all A_27a all A_27b all F0_2E0 ((all V2P_2E0 all V3x_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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))))) -> (all V0l1_2E0 all V1l2_2E0 all V2P_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))))) # label(thm_2Elist_2Eevery__zip__fst) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4227 (all A_27a all V0x_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V0x_2E0) -> s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))) # label(thm_2Elist_2EHD__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4228 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) # label(thm_2Elist_2EMAP__MAP__o) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4229 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2EDROP__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4230 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4231 (all A_27a all V0ls_2E0 all V1f_2E0 all V2n_2E0 ((all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3i_2E0))))) & s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) -> s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Elist_2EGENLIST__EL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4232 (all A_27a all V0P_2E0 all V1l_2E0 all V2n1_2E0 all V3n2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n2_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n1_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> s(tyop_2Enum_2Enum,V3n2_2E0) = s(tyop_2Enum_2Enum,V2n1_2E0))) # label(thm_2Elist_2EALL__DISTINCT__FILTER__EL__IMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4233 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4234 (all A_27a all V0n_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> (all V2m1_2E0 all V3m2_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3m2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m2_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V2m1_2E0) = s(tyop_2Enum_2Enum,V3m2_2E0))))) # label(thm_2Elist_2EALL__DISTINCT__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4235 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))) & p(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)),V1P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(A_27a,V2h_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))) & (all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Elist_2EEVERYi__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4236 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Elist_2ELIST__TO__SET__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4237 (all A_27a ((all V2i_2E0 all V3P_2E0 all V4h_2E0 all V5t_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4h_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(A_27a,V4h_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2i_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0)))))) & (all V0i_2E0 all V1P_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ENONE_2E0)))) # label(thm_2Elist_2EINDEX__FIND__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4238 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EdropWhile_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EdropWhile_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4239 (all A_27a all X0_2E0 all 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_2Epred__set_2ESUBSET_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_2Ebool,c_2Epred__set_2ESUBSET_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_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4240 (all A_27a all A_27b all F0_2E0 ((all V0x_2E0 all V2f_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)),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(A_27b,V0x_2E0)))) -> (all V0x_2E0 all V1fs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1fs_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ECONS_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)),F0_2E0),s(A_27b,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1fs_2E0)))))) # label(thm_2Elist_2ESINGL__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4241 (all A_27a all V0P_2E0 all V1l_2E0 all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V4l3_2E0 exists V5l4_2E0 (s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V5l4_2E0))) & s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V4l3_2E0))) & s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l3_2E0),s(tyop_2Elist_2Elist(A_27a),V5l4_2E0))))))) # label(thm_2Elist_2EFILTER__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4242 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = 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)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4243 (all A_27a all A_27b all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EUNZIP_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4244 (all A_27a all A_27b all V0f_2E0 all V1n_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EMAP__TAKE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4245 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EsplitAtPki_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_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_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Elist_2EdropWhile__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4246 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27c_2CA_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4247 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4248 (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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4249 (all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4250 (all A_27a all V0f_2E0 all V1P_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (exists V3i_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Elist_2EEXISTS__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4251 (all A_27a all V0f_2E0 all V1x_2E0 all V2ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))))))) # label(thm_2Elist_2ESUM__MAP__MEM__bound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4252 (all A_27h all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Elist_2Elist(A_27h)),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Elist_2Elist(A_27h))),c_2Elist_2ECONS_2E0),s(A_27h,X0_2E0))),s(tyop_2Elist_2Elist(A_27h),X1_2E0))) = s(tyop_2Elist_2Elist(A_27h),c_2Elist_2ECONS_2E2(s(A_27h,X0_2E0),s(tyop_2Elist_2Elist(A_27h),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4253 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0)))))) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27b),V1b_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0a_2E0),s(tyop_2Elist_2Elist(A_27b),V1b_2E0))))))))) # label(thm_2Elist_2EZIP__DROP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 4254 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))))) -> (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))))) & s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0))) = s(A_27a,V0x_2E0))))) # label(thm_2Elist_2Emem__exists__set) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4255 (all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4256 (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 ((all V6a0_2E0 all V7a1_2E0 (s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6a0_2E0),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0),s(A_27a,V6a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_27_2E0),s(A_27a,V6a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))))) & (s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) -> s(A_27b,V4v_2E0) = s(A_27b,V0v_27_2E0)) & s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V2M_2E0) -> s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V2M_2E0),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_27_2E0))))) # label(thm_2Elist_2Elist__case__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4257 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4258 (all A_27e all A_27f all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27e),X1_2E0),s(tyop_2Elist_2Elist(A_27f),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27e),X1_2E0))),s(tyop_2Elist_2Elist(A_27f),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4259 (all A_27a all V0e_2E0 all V1L_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_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0e_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))) # label(thm_2Elist_2EUNIQUE__LENGTH__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4260 (all A_27a all V0a0_2E0 all V1a1_2E0 all V2a0_27_2E0 all V3a1_27_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) <-> s(A_27a,V0a0_2E0) = s(A_27a,V2a0_27_2E0) & s(tyop_2Elist_2Elist(A_27a),V1a1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) # label(thm_2Elist_2Elist__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4261 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4262 (all A_27a all V0l_2E0 all 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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) <-> (exists V2n_2E0 (s(A_27a,V1x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EMEM__EL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4263 (all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4264 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) & (all V0P_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EdropWhile__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4265 (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]. 7.58/7.58 4266 (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_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4267 (all A_27a all V0x_2E0 all V1xs_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))) # label(thm_2Elist_2ELENGTH__FRONT__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4268 (all A_27a all V0ys_2E0 all V1y_2E0 all V2x_2E0 ((exists V3xs_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1y_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),V2x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V3xs_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) | s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V2x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1y_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))))) # label(thm_2Elist_2EisPREFIX__CONSR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4269 (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(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4270 (all A_27a all V0n_2E0 all V1m_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) # label(thm_2Elist_2ETAKE__SUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4271 (all A_27a all V0l_2E0 ((all V1n1_2E0 all V2n2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> (s(tyop_2Enum_2Enum,V2n2_2E0) = s(tyop_2Enum_2Enum,V1n1_2E0) <-> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EEL__ALL__DISTINCT__EL__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4272 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4273 (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]. 7.58/7.58 4274 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4275 (all A_27a all V0P_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_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_2Elist_2ENULL__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4276 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),c_2Epair_2ESND_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Elist_2EFIND__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4277 (all A_27a all A_27b all F0_2E0 ((all V0l_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,V3x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,V3x_2E0)))) -> (all V0l_2E0 all V1f_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Elist_2EZIP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4278 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2ELAST__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4279 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4280 (all A_27a all F0_2E0 ((all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(A_27a,V1x_2E0)))) -> (all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2EMAP__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4281 (all A_27a all F1_2E0 all F2_2E0 all F0_2E0 ((all V4t1_2E0 all V7t2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))))) -> ((all V3h1_2E0 all V6h2_2E0 (s(A_27a,V6h2_2E0) = s(A_27a,V3h1_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)),F2_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))))) -> ((all V4t1_2E0 all V2R_2E0 all V3h1_2E0 all V6h2_2E0 all V7t2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))),s(tyop_2Emin_2Ebool,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)),V2R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,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)),F2_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) -> (all V2R_2E0 all V3h1_2E0 all V4t1_2E0 all V5l2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),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_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0)))) & (all V0R_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))))) # label(thm_2Elist_2ESHORTLEX__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4282 (all A_27a all V0l_2E0 all V1Q_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),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4283 (all A_27a all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V2a_2E0) & s(tyop_2Elist_2Elist(A_27a),V1y_2E0) = s(tyop_2Elist_2Elist(A_27a),V3b_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V3b_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1y_2E0))))) # label(thm_2Elist_2ESNOC__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4284 (all A_27a all V0t2_2E0 all V1t1_2E0 all V2h2_2E0 all V3h1_2E0 all V4R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) | s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))) & s(A_27a,V3h1_2E0) = s(A_27a,V2h2_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)),V4R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V2h2_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ESHORTLEX__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4285 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4286 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Elist_2EINDEX__OF_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Elist_2EINDEX__OF_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EINDEX__OF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4287 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4288 (all A_27a all V0e_2E0 all V1L_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))) <-> (exists V2L1_2E0 exists V3L2_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2L1_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3L2_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2L1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3L2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1L_2E0))))) # label(thm_2Elist_2EUNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4289 (all A_27a ((all V0x_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(A_27a,V0x_2E0)) & (all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0))))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0)))))))) # label(thm_2Elist_2ELAST__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4290 (all A_27a all A_27b all A_27c all V0f_2E0 all V1ts_2E0 all V2tt_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_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ts_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2tt_2E0)))))))) -> s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ts_2E0),s(tyop_2Elist_2Elist(A_27b),V2tt_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_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ts_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27b),V2tt_2E0))))))) # label(thm_2Elist_2EEL__MAP2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4291 (all A_27a all V0h1_2E0 all V1h2_2E0 (s(A_27a,V0h1_2E0) != s(A_27a,V1h2_2E0) -> (all V2l1_2E0 all V3l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0)))))) # label(thm_2Elist_2ENOT__EQ__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4292 (all A_27a all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EDROP__nil) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4293 (all A_27a all V0P_2E0 all V1l_2E0 all V2h_2E0 all V3lr_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3lr_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V4l1_2E0 exists V5l2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))) & s(tyop_2Elist_2Elist(A_27a),V3lr_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))) & s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))))))) # label(thm_2Elist_2EFILTER__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4294 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) # label(thm_2Elist_2EFILTER__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4295 (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)),c_2Erelation_2ERC_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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))))) # label(thm_2Elist_2ESHORTLEX__total) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4296 (all A_27a all A_27b all X0_2E0 s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),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)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4297 (all A_27a all A_27b all V0m1_2E0 all V1m2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__IGNORE__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0m1_2E0),s(tyop_2Elist_2Elist(A_27a),V1m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0m1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Elist_2Elist(A_27a),V1m2_2E0)))))) # label(thm_2Elist_2ELIST__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4298 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2x_2E0 all V3l_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)),V0f_2E0),s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))),s(A_27a,V2x_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))) # label(thm_2Elist_2EFOLDL__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4299 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2l_2E0 s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V0f_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V0f_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2Elist__case__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4300 (all A_27a all A_27b all F0_2E0 ((all V1f_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(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0))),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0)))))) -> (all V0ls_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))))) # label(thm_2Elist_2EMAP__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4301 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EREVERSE__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4302 (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,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4303 (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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4304 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) # label(thm_2Elist_2EdropWhile__APPEND__EVERY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4305 (all A_27a all A_27b all A_27c all V0x_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0x_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EMAP2__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4306 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4307 (all A_27a all A_27b all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))) # label(thm_2Elist_2ELIST__REL__LENGTH) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4308 (all A_27c all A_27d all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4309 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Elist_2ESUM_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ESUM_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4310 (all A_27a all V0l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2ENULL__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4311 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4312 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4313 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4314 (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]. 7.58/7.58 4315 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4316 (all A_27a all A_27b all V0h_2E0 all V1g_2E0 all V2f_2E0 all V3ls1_2E0 all V4ls2_2E0 ((all V5x_2E0 all V6y_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V5x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V0h_2E0),s(A_27b,V6y_2E0)))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))) -> s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0),s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))))))))) # label(thm_2Elist_2ESUM__MAP__PLUS__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4317 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,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_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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_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(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_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)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4318 (all A_27a all V0l_2E0 all V1x_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) != s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) # label(thm_2Elist_2ECONS__ACYCLIC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4319 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0f_2E0)) # label(thm_2Elist_2EREVERSE__o__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4320 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4321 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X2_2E0))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4322 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4323 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4324 (all A_27a ((all V1h_2E0 all V2t_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(A_27a,V3x_2E0)))) | s(A_27a,V3x_2E0) = s(A_27a,V1h_2E0))) & (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4325 (all A_27a ((all V0h_2E0 all V1t_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) & s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(thm_2Elist_2ENULL__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4326 (all A_27a all A_27b all V0x_2E0 all V1v_27_2E0 all V2v_2E0 all V3f_2E0 ((exists V4a_2E0 exists V5l_2E0 (s(A_27b,V1v_27_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3f_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) & s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4a_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) | s(A_27b,V2v_2E0) = s(A_27b,V1v_27_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0x_2E0) <-> s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(A_27b,V2v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3f_2E0))) = s(A_27b,V1v_27_2E0))) # label(thm_2Elist_2Elist__case__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4327 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4328 (all V0ls_2E0 ((all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0ls_2E0)))))) -> s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0ls_2E0))))) # label(thm_2Elist_2ESUM__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4329 (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)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4330 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((all V3R_2E0 all V2f_2E0 all V6a_2E0 all V7b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(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,A_27b),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_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))),s(A_27a,V6a_2E0))),s(A_27c,V7b_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)),V3R_2E0),s(A_27a,V6a_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(A_27c,V7b_2E0)))))) -> ((all V3R_2E0 all V4a_2E0 all V5b_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)),V3R_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))) -> (all V0l2_2E0 all V1l1_2E0 all V2f_2E0 all V3R_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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,A_27b),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_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27c),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0l2_2E0))))))))) # label(thm_2Elist_2ELIST__REL__MAP2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4331 (all A_27a ((all V0l_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V1l_2E0 all V2n_2E0 ((exists V3h_2E0 exists V4l_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) & (all V5l_2E0 all V6n1_2E0 all V7n2_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6n1_2E0),s(tyop_2Enum_2Enum,V7n2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) <-> (exists V8l1_2E0 exists V9l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0),s(tyop_2Elist_2Elist(A_27a),V9l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V5l_2E0) & s(tyop_2Enum_2Enum,V7n2_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V9l2_2E0))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))) = s(tyop_2Enum_2Enum,V6n1_2E0))))))) # label(thm_2Elist_2ELENGTH__EQ__NUM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4332 (all A_27a ((all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EREVERSE__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4333 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ECONS_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),c_2Elist_2ECONS_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4334 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EdropWhile_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EdropWhile_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4335 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4336 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) | (exists V2h_2E0 exists V3t_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) <-> (exists V1l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) # label(thm_2Elist_2EEXISTS__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4337 (all A_27a all A_27b all F0_2E0 ((all V2P_2E0 all V4i_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_2Ebool_2E_7E_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)),V2P_2E0),s(tyop_2Enum_2Enum,V4i_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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0))),s(tyop_2Enum_2Enum,V4i_2E0)))) -> (all V0l1_2E0 all V1l2_2E0 all V2P_2E0 all V3k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l1_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_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) -> p(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)),V2P_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(A_27b,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3k_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))))) # label(thm_2Elist_2EsplitAtPki__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4338 (all A_27a all A_27b all F0_2E0 all F2_2E0 all F1_2E0 ((all V3P_2E0 all V2Q_2E0 all V4a_2E0 all V5b_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,V4a_2E0))),s(A_27b,V5b_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,V4a_2E0))),s(A_27b,V5b_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_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)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))))) -> ((all V2Q_2E0 all V8a_2E0 all V9b_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)),V2Q_2E0),s(A_27a,V8a_2E0))),s(A_27b,V9b_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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(A_27a,V8a_2E0))),s(A_27b,V9b_2E0)))) -> ((all V3P_2E0 all V6a_2E0 all V7b_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(A_27a,V6a_2E0))),s(A_27b,V7b_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)),V3P_2E0),s(A_27a,V6a_2E0))),s(A_27b,V7b_2E0)))) -> (all V0l2_2E0 all V1l1_2E0 all V2Q_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(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)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))))))) # label(thm_2Elist_2ELIST__REL__CONJ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4339 (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]. 7.58/7.58 4340 (all A_27a all A_27b all V0R_2E0 all V1LIST__REL_27_2E0 ((all V2h1_2E0 all V3h2_2E0 all V4t1_2E0 all V5t2_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,V2h1_2E0))),s(A_27b,V3h2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) -> (all V6a0_2E0 all V7a1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))))) # label(thm_2Elist_2ELIST__REL__strongind) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4341 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4342 (all A_27a all A_27b all A_27c all V0l_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0)))))) # label(thm_2Elist_2EMAP__LIST__BIND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4343 (all A_27a all A_27b all V0fs_2E0 all V1xs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V0fs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V0fs_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0)))) # label(thm_2Elist_2ELIST__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4344 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4345 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4346 (all A_27a all A_27b all V0P_2E0 all V1l1_2E0 all V2l2_2E0 all V3v1_2E0 all V4v2_2E0 all V5n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_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,V3v1_2E0))),s(A_27b,V4v2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3v1_2E0),s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,V4v2_2E0),s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) # label(thm_2Elist_2EEVERY2__LUPDATE__same) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4347 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2EAPPEND__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4348 (all A_27a all V0h_2E0 all V1t_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(A_27a,V0h_2E0)) # label(thm_2Elist_2EHD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4349 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) # label(thm_2Elist_2ELIST__EQ__MAP__PAIR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4350 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Elist_2ESET__TO__LIST__IN__MEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4351 (all A_27a all V0n_2E0 all V1ls_2E0 all V2l_2E0 (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) # label(thm_2Elist_2EEL__simp__restricted) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4352 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))) <-> (exists V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) & s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))) # label(thm_2Elist_2EMEM__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 4353 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4354 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) <-> (exists V3y_2E0 (s(A_27b,V2x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EMEM__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4355 (all A_27a ((all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))))) # label(thm_2Elist_2EAPPEND__eq__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4356 (all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4357 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))))))) # label(thm_2Elist_2EALL__DISTINCT__ZIP__SWAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4358 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EGENLIST__AUX_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EGENLIST__AUX_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4359 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ENOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4360 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ESET__TO__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ESET__TO__LIST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4361 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__RIGHT_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EPAD__RIGHT_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EPAD__RIGHT_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4362 (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]. 7.58/7.59 4363 (all A_27a all V0P_2E0 all V1l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ENOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4364 (all A_27a all V0P_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))) # label(thm_2Elist_2EHD__dropWhile) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4365 (all A_27a all V0t_2E0 all V1l2_2E0 all V2l1_2E0 all V3h_2E0 ((exists V4lt_2E0 (s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4lt_2E0))) & s(tyop_2Elist_2Elist(A_27a),V0t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4lt_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) | s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4366 (all A_27a all V0f_2E0 all V1ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))))) # label(thm_2Elist_2ESUM__IMAGE__LIST__TO__SET__upper__bound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4367 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0),s(A_27b,V0x_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0)))) # label(thm_2Elist_2ESINGL__LIST__APPLY__L) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4368 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4369 (all A_27a all V0l_2E0 ((exists V1h_2E0 exists V2t_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))) | s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2Elist__CASES) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4370 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ECONS_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4371 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l1_27_2E0 all V2l2_2E0 all V3l2_27_2E0 all V4f_2E0 all V5f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) & (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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)),V4f_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)),V5f_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))))) & s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) = s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) -> s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) # label(thm_2Elist_2EMAP2__CONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4372 (all A_27a all A_27b all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) # label(thm_2Elist_2EEVERY2__LENGTH) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4373 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V4h_2E0 all V5t_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F1_2E0),s(A_27a,V4h_2E0))),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0)))))) -> ((all V1f_2E0 all V3t0_2E0 all V4h_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F1_2E0),s(A_27a,V4h_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0))),s(A_27a,V4h_2E0)))) -> (all V0f_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V1f_2E0 all V2h0_2E0 all V3t0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h0_2E0),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(A_27b,V2h0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0))))))))) # label(thm_2Elist_2EOPT__MMAP__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4374 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Elist_2ELENGTH__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4375 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EOPT__MMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EOPT__MMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4376 (all A_27a all V0n_2E0 all V1f_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(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Elist_2EHD__GENLIST__COR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4377 (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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2EWF__SHORTLEX) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4378 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4379 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 ((s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EMAP__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4380 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2ETAKE__LENGTH__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4381 (all A_27a all F0_2E0 ((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),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))),F0_2E0),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,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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) -> (all V0P_2E0 all V1Q_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2EEVERY__CONJ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4382 (all A_27a all V0l_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EFINITE__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4383 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4384 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4385 (all A_27a all V0P_2E0 ((all V1t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))) -> (all V2h_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2Elist__INDUCT0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4386 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__IGNORE__BIND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__IGNORE__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4387 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))) # label(thm_2Elist_2ESINGL__APPLY__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4388 (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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__TO__SET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4389 (all A_27a all V0l_2E0 all V1e_2E0 ((exists V2pfx_2E0 exists V3sfx_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) # label(thm_2Elist_2EMEM__SPLIT__APPEND__first) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4390 (all A_27g all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27g),c_2Elist_2ECONS_2E2(s(A_27g,X0_2E0),s(tyop_2Elist_2Elist(A_27g),X1_2E0))) = s(tyop_2Elist_2Elist(A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Elist_2Elist(A_27g)),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Elist_2Elist(A_27g))),c_2Elist_2ECONS_2E0),s(A_27g,X0_2E0))),s(tyop_2Elist_2Elist(A_27g),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4391 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4392 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EREVERSE__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4393 (all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4394 (all A_27a all V0y_2E0 all V1x_2E0 all V2ls_2E0 all V3e_2E0 all V4R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> (exists V5z_2E0 exists V6t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V6t_2E0),s(A_27a,V5z_2E0),s(A_27a,V0y_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)),V4R_2E0),s(A_27a,V3e_2E0))),s(A_27a,V5z_2E0)))))))) # label(thm_2Elist_2ELRC__MEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4395 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4396 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V0l_2E0) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) # label(thm_2Elist_2EAPPEND__FRONT__LAST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4397 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 all V3R_27_2E0 all V4l1_27_2E0 all V5l2_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) & (all V6a_2E0 all V7b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V4l1_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)),V3R_27_2E0),s(A_27a,V6a_2E0))),s(A_27a,V7b_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,V6a_2E0))),s(A_27a,V7b_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0) -> s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0))))) # label(thm_2Elist_2ELLEX__CONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4398 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2R_2E0 ((s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0y_2E0)))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),V0y_2E0)))) # label(thm_2Elist_2ELIST__REL__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4399 (all V0n2_2E0 all V1n1_2E0 all V2a_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V1n1_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))),s(tyop_2Enum_2Enum,V0n2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,V0n2_2E0)))))) # label(thm_2Elist_2EGENLIST__PLUS__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4400 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4401 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(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(tyop_2Elist_2Elist(A_27a),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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Elist_2ELRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Elist_2ELRC_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4402 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFRONT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4403 (all A_27a all A_27b all V0n_2E0 all V1ls_2E0 all V2l_2E0 (s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2l_2E0),s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))))) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))) & s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elist_2EEL__restricted) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4404 (all A_27a all F0_2E0 ((all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V1n_2E0 all V2x_2E0 all V3xs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_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_2Elist_2Elist(A_27a),V3xs_2E0)))))))) # label(thm_2Elist_2EDROP__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4405 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4406 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4407 (all A_27a all V0xs_2E0 all V1n_2E0 all V2x_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0xs_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) # label(thm_2Elist_2ELUPDATE__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4408 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(tyop_2Elist_2Elist(A_27d),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(tyop_2Elist_2Elist(A_27d),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4409 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4410 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4411 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EsplitAtPki_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EsplitAtPki_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4412 (all A_27a all A_27b all V0R2_2E0 all V1R1_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)),V1R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,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_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0),s(A_27b,V3y_2E0))),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27b),V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Elist_2Elist(A_27b),V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0)))))))) # label(thm_2Elist_2EEVERY2__sym) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4413 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4414 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERYi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERYi_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4415 (all A_27a ((all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1P_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))))) # label(thm_2Elist_2EEVERY__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4416 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4417 (all A_27a all V0l_2E0 all V1R_2E0 -p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ELLEX__NIL2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4418 (all A_27a all F0_2E0 ((all V0f_2E0 all V2a_2E0 all V3e_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))),s(A_27a,V3e_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3e_2E0)))))) -> (all V0f_2E0 all V1ls_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2ESUM__MAP__FOLDL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4419 (all A_27a all V0l_2E0 all V1P_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EFILTER__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4420 (all A_27a all V0a0_2E0 all V1a1_2E0 all V2a0_27_2E0 all V3a1_27_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) <-> s(A_27a,V2a0_27_2E0) = s(A_27a,V0a0_2E0) & s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))) # label(thm_2Elist_2ECONS__11) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4421 (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(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4422 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4423 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> (all V2f_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_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)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))) # label(thm_2Elist_2EMAP2__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4424 (all A_27a all V0ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) # label(thm_2Elist_2EALL__DISTINCT__CARD__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4425 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) -> (all V2h1_2E0 all V3h2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) # label(thm_2Elist_2ELIST__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4426 (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_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4427 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4428 (all A_27a all V0f_2E0 all V1P_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))))))))) # label(thm_2Elist_2EEVERY__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4429 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4430 (all A_27a ((all V0e_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V2e_2E0 all V3x_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))) & (all V5e_2E0 all V6n_2E0 all V7x_2E0 all V8l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_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_2Elist_2Elist(A_27a),V8l_2E0)))))) & (all V9e_2E0 all V10n_2E0 all V11x_2E0 all V12l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V9e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11x_2E0),s(tyop_2Elist_2Elist(A_27a),V12l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V9e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V12l_2E0)))))))) # label(thm_2Elist_2ELUPDATE__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4431 (all A_27a all A_27b all A_27c all V0f_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),V0f_2E0))) & s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0))))) # label(thm_2Elist_2ELENGTH__o__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4432 (all A_27a ((all V0l1_2E0 all V1l2_2E0 all V2l1_27_2E0 all V3l2_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0) & s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0)))) & (all V4l1_2E0 all V5l2_2E0 all V6l1_27_2E0 all V7l2_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V5l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V4l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V6l1_27_2E0)))))) # label(thm_2Elist_2EAPPEND__11__LENGTH) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4433 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4434 (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]. 7.58/7.59 4435 (all A_27a all F0_2E0 ((all V1f_2E0 all V0n_2E0 all V2m_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(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2m_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2m_2E0)))))) -> (all V0n_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_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(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Elist_2EREVERSE__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4436 (all A_27a all F0_2E0 ((all V6p_2E0 all V4n_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)),F0_2E0),s(tyop_2Enum_2Enum,V6p_2E0))),s(tyop_2Enum_2Enum,V4n_2E0)))) <-> s(tyop_2Enum_2Enum,V4n_2E0) = s(tyop_2Enum_2Enum,V6p_2E0))) -> (all V0e_2E0 all V1n_2E0 all V2l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) & (all V3e_2E0 all V4n_2E0 all V5l_2E0 all V6p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))))) -> s(A_27a,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2Enum_2Enum,V6p_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V3e_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3e_2E0),s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))))))) # label(thm_2Elist_2ELUPDATE__SEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4437 (all A_27a all F0_2E0 ((all V0c_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,V0c_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)),F0_2E0),s(tyop_2Emin_2Ebool,V0c_2E0))),s(A_27a,V2x_2E0)))) -> (all V0c_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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)),F0_2E0),s(tyop_2Emin_2Ebool,V0c_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) | p(s(tyop_2Emin_2Ebool,V0c_2E0)))))) # label(thm_2Elist_2EEVERY__SIMP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4438 (all V0acc_2E0 s(tyop_2Enum_2Enum,V0acc_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0),s(tyop_2Enum_2Enum,V0acc_2E0)))) # label(thm_2Elist_2ESUM__ACC__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4439 (all V1h_2E0 all V2t_2E0 all V3acc_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2t_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V3acc_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2t_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0)))) # label(thm_2Elist_2ESUM__ACC__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4440 (all A_27a all V0e_2E0 all V1L_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0e_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))) # label(thm_2Elist_2EUNIQUE__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4441 (all A_27a all V0l_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2EDROP__LENGTH__TOO__LONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4442 (all A_27a all V0l1_2E0 all V1l1_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0))) -> (all V2l2_2E0 all V3l2_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) # label(thm_2Elist_2EAPPEND__LENGTH__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4443 (all A_27a all F0_2E0 ((all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (all V0l_2E0 all V1n_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EEL__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4444 (all A_27a all A_27b all V0v_2E0 all V1l1_2E0 all V2x_2E0 all V3l2_2E0 all V4l3_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0v_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0)))))) # label(thm_2Elist_2Elupdate__append2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4445 (all A_27a all V0x_2E0 all V1n_2E0 all V2l1_2E0 all V3l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))))) # label(thm_2Elist_2Elupdate__append) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4446 (all A_27a ((all V1l1_2E0 all V2l2_2E0 all V3h_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) & (all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2EAPPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4447 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMAP__TL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4448 (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_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elist_2ESUM__ACC_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESUM__ACC_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4449 (all A_27a (p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V0h_2E0 all V1t_2E0 -p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))))) # label(thm_2Elist_2ENULL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4450 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> (exists V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0)))))))) # label(thm_2Elist_2EEXISTS__MEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4451 (all A_27a all V0xs_2E0 all V1x_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)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(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))))))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))))) # label(thm_2Elist_2ETAKE__cons) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4452 (all A_27a all V0L_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Elist_2ELEN__LENGTH__LEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4453 (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]. 7.58/7.59 4454 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2EDROP__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4455 (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_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4456 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EFRONT__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4457 (all A_27a all A_27b all F0_2E0 ((all V0P_2E0 all V1f_2E0 all V3x_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(A_27a,V3x_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),V1f_2E0),s(A_27a,V3x_2E0)))))) -> (all V0P_2E0 all V1f_2E0 all V2l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4458 (all A_27a all V0ls_2E0 (s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) -> s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) # label(thm_2Elist_2ELAST__EL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4459 (all A_27a all V0e_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))))) # label(thm_2Elist_2EMEM__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4460 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4461 (all A_27a all V0h1_2E0 all V1h2_2E0 (s(A_27a,V1h2_2E0) = s(A_27a,V0h1_2E0) -> (all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))))))) # label(thm_2Elist_2EEQ__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4462 (all A_27a all V0xs_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))) # label(thm_2Elist_2ELENGTH__TAKE__EQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4463 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4464 (all A_27a all A_27b all V0R_2E0 all V1LIST__REL_27_2E0 ((all V2h1_2E0 all V3h2_2E0 all V4t1_2E0 all V5t2_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,V2h1_2E0))),s(A_27b,V3h2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) -> (all V6a0_2E0 all V7a1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))))) # label(thm_2Elist_2ELIST__REL__ind) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4465 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4466 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2ETAKE__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4467 (all A_27a ((all V0f_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1f_2E0 all V2a0_2E0 all V3a1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2a0_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0)))))))) # label(thm_2Elist_2Elist__size__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4468 (all A_27a all V0a_2E0 all V1b_2E0 all V2c_2E0 all V3d_2E0 all V4x_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2c_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3d_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1b_2E0))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1b_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),V0a_2E0) = s(tyop_2Elist_2Elist(A_27a),V2c_2E0) & s(tyop_2Elist_2Elist(A_27a),V3d_2E0) = s(tyop_2Elist_2Elist(A_27a),V1b_2E0))) # label(thm_2Elist_2EMEM__APPEND__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4469 (all A_27a all V0l_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_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,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EEVERY__EL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4470 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f ((all V0f_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V1f_2E0 all V2h1_2E0 all V3t1_2E0 all V4h2_2E0 all V5t2_2E0 s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ECONS_2E2(s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(A_27d,V2h1_2E0))),s(A_27e,V4h2_2E0))),s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Elist_2Elist(A_27d),V3t1_2E0),s(tyop_2Elist_2Elist(A_27e),V5t2_2E0))))) = s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,V2h1_2E0),s(tyop_2Elist_2Elist(A_27d),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ECONS_2E2(s(A_27e,V4h2_2E0),s(tyop_2Elist_2Elist(A_27e),V5t2_2E0)))))))) # label(thm_2Elist_2EMAP2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4471 (all A_27a all X0_2E0 all X1_2E0 all 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))) = 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)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4472 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2R2_2E0 all V3R1_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)),V3R1_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)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) # label(thm_2Elist_2EEVERY2__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4473 (all A_27a all V0l_2E0 ((all 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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1x_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4474 (all A_27a all V0ls_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2ECARD__LIST__TO__SET__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4475 (all 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)),c_2Emin_2E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4476 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) | (exists V1h_2E0 exists V2t_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))) # label(thm_2Elist_2Elist__nchotomy) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4477 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4478 (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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) -> (all V3ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls_2E0))))))))))) # label(thm_2Elist_2ELENGTH__FILTER__LEQ__MONO) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 4479 (all A_27a all A_27b ((all V0f_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1f_2E0 all V2h_2E0 all V3t_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2h_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))) # label(thm_2Elist_2EMAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4480 (all A_27a all A_27b ((all V0l2_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)) & (all V2x1_2E0 all V3l1_2E0 all V4x2_2E0 all V5l2_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4x2_2E0),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x1_2E0),s(A_27b,V4x2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0)))))))) & (all V1l1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EZIP__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4481 (all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4482 (all A_27a all V0c_2E0 all V1n_2E0 all V2s_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__RIGHT_2E3(s(A_27a,V0c_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2s_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2s_2E0)))))))))) # label(thm_2Elist_2EPAD__RIGHT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4483 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2f_2E0 all V3f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2EMAP__CONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4484 (all A_27a all V0l_2E0 ((s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4485 (all A_27a all V0l_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ETAKE__LENGTH__TOO__LONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4486 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__LEFT_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EPAD__LEFT_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EPAD__LEFT_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4487 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4488 (all A_27a all A_27b all F0_2E0 ((all V1x_2E0 all V0y_2E0 all V3L1_2E0 all V4L2_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))))),F0_2E0),s(A_27a,V1x_2E0))),s(A_27b,V0y_2E0))),s(tyop_2Elist_2Elist(A_27a),V3L1_2E0))),s(tyop_2Elist_2Elist(A_27b),V4L2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3L1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0y_2E0),s(tyop_2Elist_2Elist(A_27b),V4L2_2E0)))))) -> (all V0y_2E0 all V1x_2E0 all V2t_2E0 (s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))) & s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))))),F0_2E0),s(A_27a,V1x_2E0))),s(A_27b,V0y_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(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_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))))))) # label(thm_2Elist_2EUNZIP__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4489 (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]. 7.58/7.60 4490 (all A_27e all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ECONS_2E2(s(A_27e,X0_2E0),s(tyop_2Elist_2Elist(A_27e),X1_2E0))) = s(tyop_2Elist_2Elist(A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27e)),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27e))),c_2Elist_2ECONS_2E0),s(A_27e,X0_2E0))),s(tyop_2Elist_2Elist(A_27e),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27e) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4491 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2ELUPDATE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4492 (all A_27a all F0_2E0 ((all V1x_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) -> (all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),F0_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2ESINGL__LIST__APPLY__R) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4493 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ESNOC_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ESNOC_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4494 (all A_27a all A_27b all A_27c all A_27d (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ENIL_2E0) & (all V0x1_2E0 all V1l1_2E0 all V2x2_2E0 all V3l2_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2x2_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x1_2E0),s(A_27b,V2x2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))))))) # label(thm_2Elist_2EZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4495 (all A_27a all V0l_2E0 all V1x_2E0 all V2y_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2y_2E0),s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) <-> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) | (exists V4j_2E0 (s(tyop_2Enum_2Enum,V3i_2E0) != s(tyop_2Enum_2Enum,V4j_2E0) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4j_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4j_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EMEM__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4496 (all A_27a all V0list_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0list_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0))))))) # label(thm_2Elist_2Edatatype__list) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4497 (all A_27a all V0f_2E0 all V1l_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),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)))) -> s(A_27a,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EFOLDL__EQ__FOLDR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4498 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4499 (all V0L_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Elist_2ESUM__SUM__ACC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4500 (all A_27a all V0l_2E0 all V1x_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,V1x_2E0)) # label(thm_2Elist_2EEL__LENGTH__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4501 (all A_27a ((all V1h_2E0 all V2t_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3n_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 V0n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Elist_2ELEN__DEF) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4502 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1f_2E0 all V2a_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0))),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2a_2E0)))))) # label(thm_2Elist_2EITSET__eq__FOLDL__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4503 (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]. 7.58/7.60 4504 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4505 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2l_2E0 all V3f_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) <-> (exists V4l10_2E0 exists V5l20_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V4l10_2E0))) = s(tyop_2Elist_2Elist(A_27b),V1l1_2E0) & s(tyop_2Elist_2Elist(A_27b),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V5l20_2E0))) & s(tyop_2Elist_2Elist(A_27a),V2l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l10_2E0),s(tyop_2Elist_2Elist(A_27a),V5l20_2E0))))))) # label(thm_2Elist_2EMAP__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4506 (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)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4507 (all A_27a all F0_2E0 ((all V2i_2E0 all V3k_2E0 all V0ys_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V2i_2E0))),s(tyop_2Enum_2Enum,V3k_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) & s(tyop_2Enum_2Enum,V3k_2E0) = s(tyop_2Enum_2Enum,V2i_2E0))) -> (all V0ys_2E0 all V1x_2E0 all V2i_2E0 all V3k_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V1x_2E0),s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Enum_2Enum,V2i_2E0))),s(tyop_2Enum_2Enum,V3k_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(A_27a,V1x_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))))) # label(thm_2Elist_2EEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4508 (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]. 7.58/7.60 4509 (all A_27a all F0_2E0 ((all V0f_2E0 all V1g_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0))),s(A_27a,V3x_2E0)))) -> (all V0f_2E0 all V1g_2E0 all V2ls_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0))),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))))))) # label(thm_2Elist_2ESUM__MAP__PLUS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4510 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4511 (all A_27a all V0P_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_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,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))))) # label(thm_2Elist_2EFILTER__NEQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4512 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0),s(tyop_2Elist_2Elist(A_27c),X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)))),c_2Elist_2EFOLDL2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))),s(tyop_2Elist_2Elist(A_27c),X3_2E0)))) # label(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4513 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4514 (all A_27a all A_27b ((all V0f_2E0 all V1e_2E0 s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V1e_2E0)) & (all V2f_2E0 all V3e_2E0 all V4x_2E0 all V5l_2E0 s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27b,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_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)),V2f_2E0),s(A_27a,V4x_2E0))),s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27b,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))))))) # label(thm_2Elist_2EFOLDR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4515 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4516 (all A_27a all A_27d all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4517 (all A_27a all A_27b all V0R_2E0 ((all V1h1_2E0 all V2h2_2E0 all V3t1_2E0 all V4t2_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,V1h1_2E0))),s(A_27b,V2h2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V3t1_2E0),s(tyop_2Elist_2Elist(A_27b),V4t2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h1_2E0),s(tyop_2Elist_2Elist(A_27a),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V4t2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ELIST__REL__rules) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4518 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(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_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4519 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4520 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4521 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4522 (all A_27a all V0P_2E0 all V1Q_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_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)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__MEM__MONO) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4523 (all A_27a all A_27b all V0l_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0)))))) # label(thm_2Elist_2EZIP__UNZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4524 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Elist_2ETL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4525 (all A_27a all A_27b all V0x_2E0 all V1l_2E0 all V2f_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V3x0_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x0_2E0))) = s(A_27b,V0x_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EMAP__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4526 (all A_27a all A_27b all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) # label(thm_2Elist_2EEVERY2__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4527 (all A_27a all F0_2E0 ((all V0P_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),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,V2x_2E0)))))) -> (all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EEVERY__NOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4528 (all A_27a all A_27b all A_27c all V0P_2E0 ((all V7f_2E0 all V8a_2E0 all V9cs_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V7f_2E0))),s(A_27a,V8a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V9cs_2E0))))) & (all V10f_2E0 all V11a_2E0 all V12v6_2E0 all V13v7_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V10f_2E0))),s(A_27a,V11a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V12v6_2E0),s(tyop_2Elist_2Elist(A_27b),V13v7_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))))) & (all V1f_2E0 all V2a_2E0 all V3b_2E0 all V4bs_2E0 all V5c_2E0 all V6cs_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0),s(A_27a,V2a_2E0))),s(A_27b,V3b_2E0))),s(A_27c,V5c_2E0))))),s(tyop_2Elist_2Elist(A_27b),V4bs_2E0))),s(tyop_2Elist_2Elist(A_27c),V6cs_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(A_27a,V2a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3b_2E0),s(tyop_2Elist_2Elist(A_27b),V4bs_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V5c_2E0),s(tyop_2Elist_2Elist(A_27c),V6cs_2E0)))))))) -> (all V14v_2E0 all V15v1_2E0 all V16v2_2E0 all V17v3_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V14v_2E0))),s(A_27a,V15v1_2E0))),s(tyop_2Elist_2Elist(A_27b),V16v2_2E0))),s(tyop_2Elist_2Elist(A_27c),V17v3_2E0))))))) # label(thm_2Elist_2EFOLDL2__ind) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4529 (all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4530 (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]. 7.58/7.60 4531 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2ELENGTH__LT__SHORTLEX) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4532 (all A_27a all V0f_2E0 all V1n_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2x_2E0))))) # label(thm_2Elist_2EEL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4533 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ENULL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4534 (all A_27a all A_27b all A_27c all V0P_2E0 ((all V6f_2E0 all V7y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V7y_2E0))))) & (all V8f_2E0 all V9v4_2E0 all V10v5_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V8f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V9v4_2E0),s(tyop_2Elist_2Elist(A_27b),V10v5_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))))) & (all V1f_2E0 all V2h1_2E0 all V3t1_2E0 all V4h2_2E0 all V5t2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h1_2E0),s(tyop_2Elist_2Elist(A_27b),V3t1_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h2_2E0),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0)))))))) -> (all V11v_2E0 all V12v1_2E0 all V13v2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V11v_2E0))),s(tyop_2Elist_2Elist(A_27b),V12v1_2E0))),s(tyop_2Elist_2Elist(A_27c),V13v2_2E0))))))) # label(thm_2Elist_2EMAP2__ind) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4535 (all A_27a all A_27b all F0_2E0 ((all V1f_2E0 all V2x_2E0 ((exists V3y_2E0 s(A_27a,V2x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V3y_2E0)))) <-> p(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_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(A_27a,V2x_2E0)))))) -> (all V0ls_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> (exists V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2EEXISTS__LIST__EQ__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4536 (all A_27a all F0_2E0 ((all V1x_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1x_2E0)) -> (all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),F0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0))))))) # label(thm_2Elist_2ELIST__BIND__ID) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4537 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4538 (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))),c_2Ecombin_2Eo_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),c_2Ecombin_2Eo_2E2(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]. 7.58/7.60 4539 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4540 (all A_27a all A_27b all A_27c all V0f_2E0 all V1xs_2E0 all V2ys_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0),s(tyop_2Elist_2Elist(A_27b),V2ys_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2ys_2E0)))))) # label(thm_2Elist_2ELENGTH__MAP2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4541 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4542 (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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4543 (all A_27a all A_27b all A_27c ((all V0f_2E0 all V1cs_2E0 all V2c_2E0 all V3bs_2E0 all V4b_2E0 all V5a_2E0 s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V0f_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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V0f_2E0),s(A_27a,V5a_2E0))),s(A_27b,V4b_2E0))),s(A_27c,V2c_2E0))),s(tyop_2Elist_2Elist(A_27b),V3bs_2E0),s(tyop_2Elist_2Elist(A_27c),V1cs_2E0))) = s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V0f_2E0),s(A_27a,V5a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4b_2E0),s(tyop_2Elist_2Elist(A_27b),V3bs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V2c_2E0),s(tyop_2Elist_2Elist(A_27c),V1cs_2E0)))))) & (all V9v7_2E0 all V10v6_2E0 all V11f_2E0 all V12a_2E0 s(A_27a,V12a_2E0) = s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V11f_2E0),s(A_27a,V12a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V10v6_2E0),s(tyop_2Elist_2Elist(A_27b),V9v7_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))) & (all V6f_2E0 all V7cs_2E0 all V8a_2E0 s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V6f_2E0),s(A_27a,V8a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V7cs_2E0))) = s(A_27a,V8a_2E0)))) # label(thm_2Elist_2EFOLDL2__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4544 (all A_27a all F0_2E0 ((all V0f_2E0 all V2b_2E0 all V3t_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3t_2E0),s(tyop_2Enum_2Enum,V2b_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(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V3t_2E0)))) -> (all V0f_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_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(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V1a_2E0)))))))) # label(thm_2Elist_2EGENLIST__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4545 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4546 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4547 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Elist_2Elist__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2Elist__size_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4548 (all A_27a all V0P_2E0 all V1l_2E0 ((all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EEVERY__MEM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4549 (all A_27a all V0n_2E0 all V1l_2E0 (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EEL__simp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4550 (all A_27a all V0s_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Elist_2ESUM__IMAGE__eq__SUM__MAP__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4551 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4552 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4553 (all A_27a all A_27b all A_27c all V0l_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0l_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1g_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0)))))) # label(thm_2Elist_2ELIST__BIND__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4554 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X2_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4555 (all A_27a all V0a1_2E0 all V1a0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0)))) # label(thm_2Elist_2Elist__distinct) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4556 (all A_27a all V0ls_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) -> s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) = s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) # label(thm_2Elist_2ELAST__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4557 (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)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),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,A_27a),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,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4558 (all A_27a ((all V0x_2E0 all V1xs_2E0 (s(tyop_2Elist_2Elist(A_27a),V1xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))))) & (all V4x_2E0 all V5xs_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V5xs_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5xs_2E0)))))))) & (all V2x_2E0 all V3xs_2E0 (s(tyop_2Elist_2Elist(A_27a),V3xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))))))) # label(thm_2Elist_2EFRONT__CONS__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4559 (all A_27a all A_27b all A_27c all A_27d all V0l2_2E0 all V1l1_2E0 all V2g_2E0 all V3f_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) -> s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) & s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) & s(tyop_2Elist_2Elist(A_27b),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) & s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))))) # label(thm_2Elist_2EMAP__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4560 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27d))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4561 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2f_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(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)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))) # label(thm_2Elist_2EEVERY2__EVERY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4562 (all A_27a all V0P_2E0 all V1L_2E0 all V2M_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1L_2E0),s(tyop_2Elist_2Elist(A_27a),V2M_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2M_2E0)))))) # label(thm_2Elist_2EFILTER__APPEND__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4563 (all A_27a all F0_2E0 ((all V1h_2E0 all V2t_2E0 all V4h_27_2E0 all V5t_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0)))) & s(A_27a,V1h_2E0) = s(A_27a,V4h_27_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V4h_27_2E0))),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0)))))) -> (all V0l_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (all V1h_2E0 all V2t_2E0 all V3l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V3l_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))))) # label(thm_2Elist_2EisPREFIX) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4564 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4565 (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,V2n_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) <-> (exists V4ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V4ls_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) & s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4ls_2E0))))))) # label(thm_2Elist_2ENRC__LRC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4566 (all A_27a all A_27b all V0ls_2E0 all V1f_2E0 ((all V2x_2E0 all 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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_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))) -> s(A_27a,V3y_2E0) = s(A_27a,V2x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__MAP__INJ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4567 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4568 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4569 (all A_27a all A_27b all V0pl_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))))))))) # label(thm_2Elist_2ELENGTH__UNZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4570 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4571 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = 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,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4572 (all A_27a all V0l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2ELENGTH__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4573 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ESNOC__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4574 (all A_27a all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) # label(thm_2Elist_2ELENGTH__TAKE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4575 (all A_27a all A_27b all V0x_2E0 all V1n_2E0 all V2l_2E0 all V3f_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2ELUPDATE__MAP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4576 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4577 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ESNOC_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ESNOC_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4578 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4579 (all A_27a all A_27b all V0l_2E0 all V1l_27_2E0 all V2b_2E0 all V3b_27_2E0 all V4f_2E0 all V5f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0) & s(A_27b,V3b_27_2E0) = s(A_27b,V2b_2E0) & (all V6x_2E0 all V7a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_27_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)),V5f_27_2E0),s(A_27b,V7a_2E0))),s(A_27a,V6x_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)),V4f_2E0),s(A_27b,V7a_2E0))),s(A_27a,V6x_2E0))))) -> s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V4f_2E0),s(A_27b,V2b_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V5f_27_2E0),s(A_27b,V3b_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0))))) # label(thm_2Elist_2EFOLDL__CONG) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4580 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Elist_2EMEM__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4581 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ESHORTLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ESHORTLEX_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4582 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 all V2f_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0),s(A_27b,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2ELIST__BIND__THM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4583 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4584 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))) # label(thm_2Elist_2EALL__DISTINCT__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4585 (all A_27a all F0_2E0 ((all V1P_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(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))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(A_27a,V2x_2E0)))) -> (all V0l_2E0 all V1P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) # label(thm_2Elist_2ELIST__TO__SET__FILTER) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4586 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4587 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(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(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 4588 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4589 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4590 (all A_27a s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) # label(thm_2Elist_2ESET__TO__LIST__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4591 (all A_27a all V0l_2E0 all V1R_2E0 -p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ESHORTLEX__NIL2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4592 (all A_27a all V0a1_2E0 all V1a0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0)))) # label(thm_2Elist_2ENOT__NIL__CONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4593 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELLEX_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4594 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ELIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4595 (all A_27a all V0l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) # label(thm_2Elist_2ECONS) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4596 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Erelation_2EWFREC_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)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(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)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)))),c_2Erelation_2EWFREC_2E0),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)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4597 (all A_27a all F0_2E0 ((all V1h_2E0 all V2v1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0),s(A_27a,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),V2v1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1h_2E0)))) -> (all V0l_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EoHD__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4598 (all A_27a all V0y_2E0 all V1x_2E0 all V2R2_2E0 all V3R1_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)),V3R1_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)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0))))))) # label(thm_2Elist_2ELLEX__MONO) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4599 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2R2_2E0 all V3R1_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)),V3R1_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)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) # label(thm_2Elist_2ELIST__REL__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4600 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_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)),c_2Epred__set_2Ecount_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecount_2E1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4601 (all A_27a all V0x_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2ESET__TO__LIST__SING) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4602 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2EREVERSE__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4603 (all A_27a all A_27b all F0_2E0 ((all V1f_2E0 all V3x_2E0 all V4y_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(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0))),s(A_27b,V3x_2E0))),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0),s(A_27b,V3x_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27a,V4y_2E0)))))) -> (all V0ls_2E0 all V1f_2E0 all V2e_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0),s(A_27b,V2e_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0))),s(A_27b,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2EFOLDL__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4604 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Elist_2ESET__TO__LIST__CARD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4605 (all A_27a all V0P_2E0 all V1x_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_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,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4606 (all A_27a ((all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V1l_2E0 all V2n_2E0 ((exists V3h_2E0 exists V4l_27_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) & (all V5l_2E0 all V6n_2E0 ((exists V7h_2E0 exists V8l_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V5l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7h_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))))) & (all V9l_2E0 all V10n1_2E0 all V11n2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V9l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V10n1_2E0),s(tyop_2Enum_2Enum,V11n2_2E0))) <-> (exists V12l1_2E0 exists V13l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V12l1_2E0))) = s(tyop_2Enum_2Enum,V10n1_2E0) & s(tyop_2Elist_2Elist(A_27a),V9l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V12l1_2E0),s(tyop_2Elist_2Elist(A_27a),V13l2_2E0))) & s(tyop_2Enum_2Enum,V11n2_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V13l2_2E0))))))))) # label(thm_2Elist_2ELENGTH__EQ__NUM__compute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4607 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4608 (all A_27a all 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))) = 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)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4609 (all A_27a all V0y_2E0 all V1x_2E0 all V2R2_2E0 all V3R1_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)),V3R1_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)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0))))))) # label(thm_2Elist_2ESHORTLEX__MONO) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4610 (all A_27a all V0ls_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__FLAT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4611 (all A_27a all F0_2E0 ((all V0t_2E0 (s(tyop_2Elist_2Elist(A_27a),V0t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0)))))) -> (all V0t_2E0 all V1h_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))),s(A_27a,V1h_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0t_2E0)))))))) # label(thm_2Elist_2ELAST__CONS__cond) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4612 (all A_27a all V0l_2E0 all V1x_2E0 all V2y_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2y_2E0),s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) | s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) # label(thm_2Elist_2EMEM__LUPDATE__E) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4613 (all A_27a all X0_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4614 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ETAKE__DROP) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4615 (all A_27a all V0l_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2Enub__set) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4616 (all A_27a all A_27b all V0f0_2E0 all V1f1_2E0 exists V2fn_2E0 ((all V3a0_2E0 all V4a1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a0_2E0),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),V1f1_2E0),s(A_27a,V3a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0)))))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V0f0_2E0))) # label(thm_2Elist_2Elist__Axiom) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4617 (all A_27a all V0x_2E0 all V1n_2E0 all V2ys_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2ys_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2ys_2E0)))))) # label(thm_2Elist_2ELENGTH__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4618 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4619 (all A_27a all V0M_2E0 all V1N_2E0 all V2f_2E0 all V3f_27_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1N_2E0)))))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V1N_2E0) = s(tyop_2Elist_2Elist(A_27a),V0M_2E0) -> s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0M_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1N_2E0))))) # label(thm_2Elist_2Elist__size__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 4620 (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]. 7.68/7.61 4621 (all A_27a all V0h_2E0 all V1l1_2E0 all V2l2_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2ELAST__APPEND__CONS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4622 (all A_27a all V0xs_2E0 all V1n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Elist_2EoEL__THM) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4623 (all A_27a all F0_2E0 ((all V0c_2E0 all V2x_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)),F0_2E0),s(tyop_2Emin_2Ebool,V0c_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,V0c_2E0)) -> (all V0c_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_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)),F0_2E0),s(tyop_2Emin_2Ebool,V0c_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),V1l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & p(s(tyop_2Emin_2Ebool,V0c_2E0)))))) # label(thm_2Elist_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4624 (all A_27a all V0l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) <-> (exists V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))))) # label(thm_2Elist_2ENOT__NULL__MEM) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4625 (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]. 7.68/7.61 4626 (all A_27a all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4627 (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]. 7.68/7.61 4628 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((all V7n_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0),s(tyop_2Enum_2Enum,V7n_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)) -> ((all V4n_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)) -> ((all V1a0_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0)))) <-> (all V2_27list_27_2E0 ((all V3a0_27_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) | (exists V5a0_2E0 exists V6a1_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(A_27a,V5a0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0))))) = s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0)))))))) -> (exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),V0rep_2E0))))))))) # label(thm_2Elist_2Elist__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4629 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4630 (all A_27a all V0P_2E0 all V1xs_2E0 all V2h_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2h_2E0),s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))))))) # label(thm_2Elist_2EIMP__EVERY__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4631 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(A_27b),V4y_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(A_27b),V4y_2E0)))) -> (all V0f_2E0 all V1ls_2E0 all V2a_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Elist_2Elist(A_27b),V2a_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27b),V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2EFOLDR__CONS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4632 (all A_27a ((all V0e_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V2e_2E0 all V3x_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))) & (all V5e_2E0 all V6n_2E0 all V7x_2E0 all V8l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0)))))))) # label(thm_2Elist_2ELUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4633 (all A_27a all V0x_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__SNOC) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4634 (all A_27a all V0l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4635 (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))),c_2Epred__set_2EDIFF_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),c_2Epred__set_2EDIFF_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_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4636 (all A_27a all V0P_2E0 all V1ls_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))),s(tyop_2Enum_2Enum,V2k_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) # label(thm_2Elist_2EEL__LENGTH__dropWhile__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4637 (all A_27a all V0y_2E0 all V1x_2E0 all V2t_2E0 all V3h_2E0 all V4e_2E0 all V5R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> (exists V6z_2E0 exists V7p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(tyop_2Elist_2Elist(A_27a),V7p_2E0),s(A_27a,V1x_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)),V5R_2E0),s(A_27a,V6z_2E0))),s(A_27a,V4e_2E0)))))))) # label(thm_2Elist_2ELRC__MEM__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4638 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0x_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Elist_2EINDEX__OF_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Elist_2EINDEX__OF__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4639 (all A_27c all X0_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4640 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4641 (all A_27a ((all V0x_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1x_2E0 all V2x_27_2E0 all V3l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))))) # label(thm_2Elist_2ESNOC) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4642 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 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_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4643 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4644 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2EUNION__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4645 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4646 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) # label(thm_2Elist_2ELENGTH__ZIP) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4647 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4648 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4649 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4650 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))) -> (all V2h_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2Elist__INDUCT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4651 (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,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),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)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4652 (all A_27a ((all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))) & (all V3R_2E0 all V4h_2E0 all V5t_2E0 all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))) <-> (exists V8z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0),s(A_27a,V8z_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)),V3R_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0)))))) & s(A_27a,V6x_2E0) = s(A_27a,V4h_2E0))))) # label(thm_2Elist_2ELRC__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4653 (all A_27a all V0n_2E0 all V1f_2E0 all V2g_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0),s(tyop_2Enum_2Enum,V3x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3x_2E0))))))) # label(thm_2Elist_2EGENLIST__FUN__EQ) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4654 (all A_27a all F0_2E0 ((all V1t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1t_2E0))) -> (all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))))) # label(thm_2Elist_2EFRONT__DEF) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4655 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4656 (all A_27a all F0_2E0 ((all V0L1_2E0 all V1L2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0)))) <-> (exists V2h_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1L2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0)))))) # label(thm_2Elist_2EWF__LIST__PRED) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4657 (all A_27a (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & (all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),V1t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))) # label(thm_2Elist_2ETL__DEF) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4658 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4659 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4660 (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)))))) -> (all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V6z_2E0)))))))) # label(thm_2Elist_2EEVERY2__trans) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4661 (all A_27a ((all V1f_2E0 all V2n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_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)))))) & (all V0f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EGENLIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4662 (all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0))) = s(tyop_2Elist_2Elist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d))),c_2Elist_2ECONS_2E0),s(A_27d,X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4663 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4664 (all A_27a all V0n_2E0 all V1f_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Elist_2EHD__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4665 (all A_27a ((all V0l_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (all V1l_2E0 all V2n_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EEL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4666 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4667 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4668 (all A_27a all A_27b all V0xs_2E0 all V1t_2E0 all V2h_2E0 all V3R_2E0 ((exists V4h_27_2E0 exists V5t_27_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_27_2E0))) = s(tyop_2Elist_2Elist(A_27b),V0xs_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_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)),V3R_2E0),s(A_27a,V2h_2E0))),s(A_27b,V4h_27_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0)))))) # label(thm_2Elist_2ELIST__REL__CONS1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4669 (all A_27a all V0L_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EREVERSE__REV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4670 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4671 (all A_27a ((all V5f_2E0 all V6n_2E0 all V7l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V7l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V7l_2E0)))) & (all V2f_2E0 all V3n_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_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_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_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_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))) & (all V0f_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2EGENLIST__AUX__compute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4672 (all A_27a all V0xs_2E0 all V1x_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)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(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))))))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) # label(thm_2Elist_2EDROP__cons) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4673 (all A_27a all V0xs_2E0 all V1x_2E0 all V2y_2E0 all V3ys_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V1x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0)))))) # label(thm_2Elist_2ELUPDATE__LENGTH) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4674 (all A_27a all F0_2E0 ((all V0P_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,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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))))) -> (all V0P_2E0 all V1l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EEXISTS__NOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4675 (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]. 7.68/7.61 4676 (all A_27a all V0l_2E0 all V1P_2E0 ((all V3h_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3h_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) & (all V2h_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EFILTER__COND__REWRITE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4677 (all A_27a all X0_2E0 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_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(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)),tyop_2Emin_2Ebool),X0_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(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)),tyop_2Emin_2Ebool),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_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(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)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4678 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4679 (all A_27a ((all V0P_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1P_2E0 all V2h_2E0 all V3t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))) # label(thm_2Elist_2EFILTER) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4680 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,V1n_2E0)) # label(thm_2Elist_2ELENGTH__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4681 (all A_27a all V0l_2E0 all V1Q_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),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMONO__EVERY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4682 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4683 (all A_27a all V0L1_2E0 all V1L2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0)))) # label(thm_2Elist_2EREV__REVERSE__LEM) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4684 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4685 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0)))))) # label(thm_2Elist_2EMAP__o) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4686 (all A_27a all A_27b ((all V2a0_2E0 all V3a1_2E0 all V4v_2E0 all V5f_2E0 s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0))),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0),s(A_27a,V2a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0)))) & (all V0v_2E0 all V1f_2E0 s(A_27b,V0v_2E0) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_2E0)))))) # label(thm_2Elist_2Elist__case__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4687 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4688 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4689 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2P_2E0 all V3P_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_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,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) # label(thm_2Elist_2EEXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4690 (all A_27a all F0_2E0 ((all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (all V1n_2E0 all V2x_2E0 all V3xs_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_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_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0)))))) & (all V0n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EoEL__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4691 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4692 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4693 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4694 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4695 (all A_27a all F0_2E0 ((all V0l1_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),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27a,V2x_2E0)))))) -> (all V0l1_2E0 all V1l2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) # label(thm_2Elist_2Elist__to__set__diff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4696 (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]. 7.68/7.61 4697 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4698 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EFILTER__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4699 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2l1_2E0 all V3l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))) # label(thm_2Elist_2EEVERY2__MEM__MONO) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4700 (all A_27a all A_27b all V0bs_2E0 all V1b_2E0 all V2as_2E0 all V3a_2E0 all V4R_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_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)),V4R_2E0),s(A_27a,V3a_2E0))),s(A_27b,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1b_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0))))))) & s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1b_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Elist_2ELIST__REL__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4701 (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]. 7.68/7.61 4702 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4703 (all A_27a all V0x_2E0 all V1n_2E0 all V2f_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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) <-> (exists V3m_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3m_2E0))) = s(A_27a,V0x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Elist_2EMEM__GENLIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4704 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4705 (all A_27a (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V0h_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))))) # label(thm_2Elist_2EALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4706 (all A_27a all V0l_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EMEM__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.61 4707 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4708 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((all V3s_2E0 all V0f_2E0 all V4x_2E0 all V5y_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,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_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0))),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> ((all V0f_2E0 all V3s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,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_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,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_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0)))))) -> (all V0f_2E0 all V1ls_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1ls_2E0))))))))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1ls_2E0))))))) # label(thm_2Elist_2EFOLDL__UNION__BIGUNION__paired) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4709 (all A_27a all A_27b all A_27c all F0_2E0 ((all V2f_2E0 all V4a_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)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V4a_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0))),s(A_27c,V4a_2E0)))) -> (all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (all V2f_2E0 all V3a_2E0 s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(A_27c,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0))),s(A_27c,V3a_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))))) # label(thm_2Elist_2EFOLDL2__FOLDL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4710 (all A_27a all F1_2E0 all F0_2E0 ((all V3h1_2E0 all V6h2_2E0 (s(A_27a,V3h1_2E0) = s(A_27a,V6h2_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)),F1_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0)))))) -> ((all V2R_2E0 all V3h1_2E0 all V4t1_2E0 all V6h2_2E0 all V7t2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))) = s(tyop_2Emin_2Ebool,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)),V2R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,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)),F1_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) -> (all V0R_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) & (all V2R_2E0 all V3h1_2E0 all V4t1_2E0 all V5l2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(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(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3h1_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))))))) # label(thm_2Elist_2ELLEX__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4711 (all A_27a all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EEL__REVERSE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4712 (all A_27a all A_27b all V0ps_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))))) # label(thm_2Elist_2EMEM__ZIP__MEM__MAP) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4713 (all A_27a all V0l1_2E0 all V1l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) & (all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__APPEND) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4714 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ewhile_2EOLEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2EOLEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4715 (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 V1l_2E0 all V2s_2E0 ((exists V4a_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0))))) & (all V3d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V3d_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Enum_2Enum,V1l_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3d_2E0))))) -> (exists V5b_2E0 ((all V6c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6c_2E0),s(tyop_2Elist_2Elist(A_27a),V5b_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V6c_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V5b_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Elist_2EWF__SHORTLEX__same__lengths) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4716 (all A_27a all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) # label(thm_2Elist_2ETAKE__nil) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4717 (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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBIT__MODIFY_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EBIT__MODIFY_2E3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4718 (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]. 7.68/7.62 4719 (all V0f_2E0 ((all V5n_2E0 all V6x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V5n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V6x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))),s(tyop_2Enum_2Enum,V6x_2E0)))) & (all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,V4x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))))) & (all V2y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) & (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4720 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4721 (all V1n_2E0 all V2m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4722 (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]. 7.68/7.62 4723 (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_2Ebit_2EBIT__REVERSE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBIT__REVERSE_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4724 (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]. 7.68/7.62 4725 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4726 (all V2n_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V3x_2E0),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,c_2Earithmetic_2E_2B_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,V4y_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V4y_2E0)))) # label(thm_2Enumeral__bit_2EBIT__REV__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4727 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,V1y_2E0)) # label(thm_2Enumeral__bit_2EBIT__REV__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4728 (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]. 7.68/7.62 4729 (all A_27a ((all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & (all V3x_2E0 all V4n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_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,V4n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))) & (all V5x_2E0 all V6n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))),s(tyop_2Enum_2Enum,V6n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0)))))) & (all V7x_2E0 all V8n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V8n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7x_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_2ESUC_2E1(s(tyop_2Enum_2Enum,V8n_2E0)))))))) & (all V9x_2E0 all V10n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0)))))) & (all V1x_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__imod__2exp) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4730 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiSUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EiSUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4731 (all V0a_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Enumeral__bit_2EMOD__2EXP__MAX_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4732 (all V1n_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V2a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V2a_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))))) # label(thm_2Enumeral__bit_2EMOD__2EXP__MAX_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4733 (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]. 7.68/7.62 4734 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4735 (all 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))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4736 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elogroot_2ELOG_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4737 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Ebit_2EMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4738 (all V0a_2E0 all V1b_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4739 (all V5n_2E0 all V6a_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Enum_2Enum,V6a_2E0),s(tyop_2Enum_2Enum,V6a_2E0)))) # label(thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4740 (all V2n_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))) <-> s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3a_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V4b_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V3a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V4b_2E0)))))))) # label(thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4741 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOWEST__SET__BIT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOWEST__SET__BIT_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4742 (all V5n_2E0 all V6f_2E0 all V7x_2E0 all V8b_2E0 all V9e_2E0 all V10y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V7x_2E0),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,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V8b_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_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,V9e_2E0))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,V8b_2E0))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V9e_2E0),s(tyop_2Enum_2Enum,V10y_2E0))),s(tyop_2Enum_2Enum,V10y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V5n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,V7x_2E0),s(tyop_2Enum_2Enum,V8b_2E0),s(tyop_2Enum_2Enum,V9e_2E0),s(tyop_2Enum_2Enum,V10y_2E0)))) # label(thm_2Enumeral__bit_2EBIT__MODF__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4743 (all V0f_2E0 all V1x_2E0 all V2b_2E0 all V3e_2E0 all V4y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V3e_2E0),s(tyop_2Enum_2Enum,V4y_2E0))) = s(tyop_2Enum_2Enum,V4y_2E0)) # label(thm_2Enumeral__bit_2EBIT__MODF__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4744 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__ilog2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4745 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__ilog2_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4746 (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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4747 (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]. 7.68/7.62 4748 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,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_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumeral__bit_2ESFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumeral__bit_2ESFUNPOW_2E3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4749 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = 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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ecombin_2EFAIL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4750 (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]. 7.68/7.62 4751 (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]. 7.68/7.62 4752 (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]. 7.68/7.62 4753 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,V1y_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4754 (all V4n_2E0 all V5y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V5y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V5y_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4755 (all V6n_2E0 all V7x_2E0 all V8y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7x_2E0))),s(tyop_2Enum_2Enum,V8y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_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_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V7x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8y_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V8y_2E0)))))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4756 (all V9n_2E0 all V10x_2E0 all V11y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V10x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V11y_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V11y_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V10x_2E0))),s(tyop_2Enum_2Enum,V11y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4757 (all V2n_2E0 all V3y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(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))))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V3y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4758 (all V0m_2E0 all V1f_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_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)))) # label(thm_2Enumeral__bit_2EBIT__MODIFY__EVAL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4759 (all A_27a ((all V0x_2E0 all V1f_2E0 all V2a_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) & (all V3x_2E0 all V4f_2E0 all V5a_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) & (all V6x_2E0 all V7f_2E0 all V8b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V6x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V7f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V6x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V7f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8b_2E0)))))) & (all V9x_2E0 all V10f_2E0 all V11a_2E0 all V12b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V9x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V10f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V12b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V9x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V10f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V12b_2E0)))))))))) # label(thm_2Enumeral__bit_2ENUMERAL__BITWISE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4760 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Ebit_2ETIMES__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ETIMES__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4761 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EiDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4762 (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]. 7.68/7.62 4763 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4764 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4765 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4766 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4767 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Enumeral__bit_2Enumeral__mod2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4768 (all 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,V0n_2E0))))),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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__mod2_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4769 (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]. 7.68/7.62 4770 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumeral__bit_2EBIT__REV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumeral__bit_2EBIT__REV_2E3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4771 (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]. 7.68/7.62 4772 (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_2Ebit_2EDIV__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EDIV__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4773 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 all X5_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),c_2Enumeral__bit_2EBIT__MODF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))),s(tyop_2Enum_2Enum,X4_2E0))),s(tyop_2Enum_2Enum,X5_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0),s(tyop_2Enum_2Enum,X4_2E0),s(tyop_2Enum_2Enum,X5_2E0)))) # label(arityeq6_2Ec_2Enumeral__bit_2EBIT__MODF_2E6) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4774 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4775 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4776 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral__bit_2EFDUB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EFDUB_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4777 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4778 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))))) # label(thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4779 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4780 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,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_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4781 (all F0_2E0 ((all V1m_2E0 all 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)),F0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) <-> s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) -> (all V0base_20_3C_202_20or_20n_20_3D_200_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_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_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ELOG_2E0),s(tyop_2Emin_2Ebool,V0base_20_3C_202_20or_20n_20_3D_200_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Enumeral__bit_2ELOG__compute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4782 (all V0f_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0)))))) & (all V3x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3x_2E0)))))))) & (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))))))) # label(thm_2Enumeral__bit_2EFDUB__FDUB) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4783 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Enumeral__bit_2EiBITWISE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Enumeral__bit_2EiBITWISE_2E4) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4784 (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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral__bit_2EFDUB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral__bit_2EFDUB_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4785 (all F0_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V4x_2E0))) -> (all V2f_2E0 all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V4x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4x_2E0)))) & (all V0f_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))))) # label(thm_2Enumeral__bit_2ESFUNPOW__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4786 (all V0i_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0i_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0i_2E0)))))) # label(thm_2Enumeral__bit_2EiDUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4787 (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]. 7.68/7.62 4788 (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]. 7.68/7.62 4789 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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))))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumeral__bit_2EiLOG2__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4790 (all V0n_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Enumeral__bit_2EDIV__2EXP) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4791 (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]. 7.68/7.62 4792 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ebit_2EMOD__2EXP__EQ_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EMOD__2EXP__EQ_2E3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4793 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral__bit_2EFDUB__iDIV2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4794 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4795 (all V4n_2E0 all V5x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,V5x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V5x_2E0)))))))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4796 (all V2n_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,V3x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V3x_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4797 (all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4798 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiLOG2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EiLOG2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4799 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiDUB_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4800 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4801 (all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4802 (all V4n_2E0 all V5x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,V5x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4803 (all V2n_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,V3x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4804 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4805 (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]. 7.68/7.62 4806 (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_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4807 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) # label(thm_2Enumeral__bit_2ELOWEST__SET__BIT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4808 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral__bit_2EFDUB__iDUB) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4809 (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]. 7.68/7.62 4810 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Enumeral__bit_2EBIT__REVERSE__EVAL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4811 (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]. 7.68/7.62 4812 (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]. 7.68/7.62 4813 (all V1x_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Enumeral__bit_2EMOD__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4814 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2EMOD__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4815 (all V2m_2E0 all V3f_2E0 all V4n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_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_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4816 (all V0m_2E0 all V1f_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_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)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4817 (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_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4818 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebit_2EBITWISE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Ebit_2EBITWISE_2E4) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4819 (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_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESBIT_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ESBIT_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4820 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4821 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4822 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Enumeral__bit_2Enumeral__log2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4823 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__log2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4824 (all V0f_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2EFDUB__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4825 (all V1f_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Enumeral__bit_2EFDUB__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4826 (all V0f_2E0 all V1x_2E0 all V2b_2E0 all V3e_2E0 all V4y_2E0 s(tyop_2Enum_2Enum,V4y_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V3e_2E0),s(tyop_2Enum_2Enum,V4y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4827 (all V5n_2E0 all V6f_2E0 all V7b_2E0 all V8e_2E0 all V9y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V7b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8e_2E0))),s(tyop_2Enum_2Enum,V9y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V7b_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_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V8e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,V7b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8e_2E0))),s(tyop_2Enum_2Enum,V9y_2E0))),s(tyop_2Enum_2Enum,V9y_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4828 (all V15n_2E0 all V16f_2E0 all V17x_2E0 all V18b_2E0 all V19e_2E0 all V20y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V15n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V16f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17x_2E0))),s(tyop_2Enum_2Enum,V18b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19e_2E0))),s(tyop_2Enum_2Enum,V20y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V15n_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V16f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V18b_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_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V19e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V16f_2E0),s(tyop_2Enum_2Enum,V18b_2E0))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V17x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19e_2E0))),s(tyop_2Enum_2Enum,V20y_2E0))),s(tyop_2Enum_2Enum,V20y_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4829 (all V21n_2E0 all V22f_2E0 all V23x_2E0 all V24b_2E0 all V25e_2E0 all V26y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V21n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V22f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V23x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V24b_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_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V25e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V22f_2E0),s(tyop_2Enum_2Enum,V24b_2E0))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V23x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25e_2E0))),s(tyop_2Enum_2Enum,V26y_2E0))),s(tyop_2Enum_2Enum,V26y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V21n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V22f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V23x_2E0))),s(tyop_2Enum_2Enum,V24b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25e_2E0))),s(tyop_2Enum_2Enum,V26y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4830 (all V10n_2E0 all V11f_2E0 all V12b_2E0 all V13e_2E0 all V14y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V12b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V13e_2E0))),s(tyop_2Enum_2Enum,V14y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V12b_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_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V13e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11f_2E0),s(tyop_2Enum_2Enum,V12b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V13e_2E0))),s(tyop_2Enum_2Enum,V14y_2E0))),s(tyop_2Enum_2Enum,V14y_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4831 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,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_2Enumeral__bit_2EiMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral__bit_2EiMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4832 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOG2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOG2_2E1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4833 (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]. 7.68/7.62 4834 (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]. 7.68/7.62 4835 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Enumeral__bit_2ENUMERAL__iDIV2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4836 (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]. 7.68/7.62 4837 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_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)),c_2Ebit_2EMOD__2EXP__MAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP__MAX_2E2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4838 (all F1_2E0 all F0_2E0 ((all V9opr_2E0 all V10a_2E0 all V11b_2E0 all V12w_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),V9opr_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V10a_2E0))))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V11b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V12w_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V12w_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0))),s(tyop_2Enum_2Enum,V10a_2E0))),s(tyop_2Enum_2Enum,V11b_2E0))),s(tyop_2Enum_2Enum,V12w_2E0)))) -> ((all V4opr_2E0 all V5a_2E0 all V6b_2E0 all V7w_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0))),s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,V6b_2E0))),s(tyop_2Enum_2Enum,V7w_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),V4opr_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V5a_2E0))))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V6b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7w_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V7w_2E0)))))) -> (all V3x_2E0 all V4opr_2E0 all V5a_2E0 all V6b_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0))),s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,V6b_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_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_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V6b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0),s(tyop_2Enum_2Enum,V5a_2E0),s(tyop_2Enum_2Enum,V6b_2E0)))) & (all V8x_2E0 all V9opr_2E0 all V10a_2E0 all V11b_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0))),s(tyop_2Enum_2Enum,V10a_2E0))),s(tyop_2Enum_2Enum,V11b_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V10a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V11b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0),s(tyop_2Enum_2Enum,V10a_2E0),s(tyop_2Enum_2Enum,V11b_2E0)))) & (all V0opr_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0opr_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) # label(thm_2Enumeral__bit_2EiBITWISE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.62 4839 (all A_27a all F0_2E0 all F1_2E0 ((all V0P_2E0 all V2x_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)),F0_2E0),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)))) -> ((all V3x_2E0 all V4s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_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)),F1_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) -> (all V0P_2E0 all V1sos_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),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)),F1_2E0),s(A_27a,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_2Eres__quan_2ERES__FORALL__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4840 (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]. 7.68/7.63 4841 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Eres__quan_2ERES__EXISTS__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4842 (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]. 7.68/7.63 4843 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4844 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((all V0P_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V4x_2E0)))) -> ((all V0P_2E0 all V3s_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) -> ((all V0P_2E0 all V2x_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)),F0_2E0),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)))) -> (all V0P_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))))) # label(thm_2Eres__quan_2ERES__FORALL__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4845 (all A_27a all F0_2E0 ((all V0x_2E0 all V2s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> (all V0x_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),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)),F0_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),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))))))) # label(thm_2Eres__quan_2EIN__BIGINTER__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4846 (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]. 7.68/7.63 4847 (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]. 7.68/7.63 4848 (all A_27a all A_27b all A_27c all F0_2E0 ((all V3s_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),F0_2E0),s(A_27c,V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2x_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),F0_2E0))))))) # label(thm_2Eres__quan_2ERES__EXISTS__F) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4849 (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]. 7.68/7.63 4850 (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]. 7.68/7.63 4851 (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]. 7.68/7.63 4852 (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]. 7.68/7.63 4853 (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]. 7.68/7.63 4854 (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]. 7.68/7.63 4855 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4856 (all A_27a all V0p_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4857 (all A_27a all V0p_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4858 (all A_27a all A_27b all F3_2E0 all F0_2E0 all F2_2E0 all F1_2E0 ((all V2R_2E0 all V3i_2E0 all V4j_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))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3i_2E0))),s(A_27b,V4j_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)),V2R_2E0),s(A_27a,V3i_2E0))),s(A_27b,V4j_2E0)))) -> ((all V1Q_2E0 all V2R_2E0 all V3i_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)),app_2E2(s(tyop_2Emin_2Efun(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_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3i_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_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))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3i_2E0)))))) -> ((all V2R_2E0 all V5j_2E0 all V6i_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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27b,V5j_2E0))),s(A_27a,V6i_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)),V2R_2E0),s(A_27a,V6i_2E0))),s(A_27b,V5j_2E0)))) -> ((all V0P_2E0 all V2R_2E0 all V5j_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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27b,V5j_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)),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(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27b,V5j_2E0)))) -> (all V0P_2E0 all V1Q_2E0 all V2R_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),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(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_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),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)),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(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4859 (all A_27a all A_27b all A_27c all F0_2E0 ((all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0),s(A_27b,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4860 (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]. 7.68/7.63 4861 (all A_27a all F0_2E0 ((all V1m_2E0 all V2x_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)),F0_2E0),s(tyop_2Emin_2Ebool,V1m_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,V1m_2E0)) -> (all V0p_2E0 all V1m_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V1m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V1m_2E0)) & (exists V3x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NULL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4862 (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]. 7.68/7.63 4863 (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]. 7.68/7.63 4864 (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]. 7.68/7.63 4865 (all A_27a all A_27b all A_27c all F0_2E0 ((all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0),s(A_27b,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0))))))) # label(thm_2Eres__quan_2ERES__FORALL__T) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4866 (all A_27a all F0_2E0 ((all V0x_2E0 all V2s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_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)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> (all V0x_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),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)),F0_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),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))))))) # label(thm_2Eres__quan_2EIN__BIGUNION__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4867 (all A_27a all V0p_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4868 (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]. 7.68/7.63 4869 (all A_27a all F0_2E0 all F3_2E0 all F2_2E0 all F1_2E0 ((all V0P_2E0 all V1Q_2E0 all V3j_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3j_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3j_2E0)))) <-> p(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))),F0_2E0),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,V3j_2E0)))))) -> ((all V2R_2E0 all V4i_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)),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V4i_2E0)))) -> ((all V2R_2E0 all V6i_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V6i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V6i_2E0)))) -> ((all V2R_2E0 all V5i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V5i_2E0)))) -> (all V0P_2E0 all V1Q_2E0 all V2R_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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)),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))))))))))))) # label(thm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4870 (all A_27a all A_27b all V0p_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0)))) # label(thm_2Eres__quan_2ERES__ABSTRACT__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4871 (all A_27a all A_27b all V0p_2E0 all V1m1_2E0 all V2m2_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0),s(A_27a,V3x_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0))))) # label(thm_2Eres__quan_2ERES__ABSTRACT__EQUAL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4872 (all A_27a all F0_2E0 ((all V0P_2E0 all V2i_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2i_2E0)))) -> (all V0P_2E0 all V1j_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1j_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1j_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Eres__quan_2ERES__FORALL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4873 (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]. 7.68/7.63 4874 (all A_27a all A_27b all V0p_2E0 all V1m1_2E0 all V2m2_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Eres__quan_2ERES__ABSTRACT__EQUAL__EQ) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4875 (all A_27a all F0_2E0 ((all V1x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> (all V0p_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),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),F0_2E0)))))) # label(thm_2Eres__quan_2ERES__SELECT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4876 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4877 (all A_27a all A_27b all A_27c all F0_2E0 ((all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0),s(A_27b,V3x_2E0)))) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0)))))))) # label(thm_2Eres__quan_2ERES__FORALL__F) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4878 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((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,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4y_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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) -> ((all V0P_2E0 all V1f_2E0 all V3x_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))),F1_2E0),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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))),s(A_27a,V3x_2E0)))))) -> ((all V1f_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))),s(A_27a,V2x_2E0)))) -> (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),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))),F1_2E0),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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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)))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4879 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4880 (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]. 7.68/7.63 4881 (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]. 7.68/7.63 4882 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__FORALL__UNION) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4883 (all A_27a all V0p_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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),V1m_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),V1m_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),V1m_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),V1m_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__ALT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4884 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4885 (all A_27a all A_27b all V0m_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0)))) # label(thm_2Eres__quan_2ERES__ABSTRACT__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4886 (all A_27a all F0_2E0 ((all V0P_2E0 all V2i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2i_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2i_2E0)))) -> (all V0P_2E0 all V1j_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1j_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1j_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4887 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((all V1s_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27b,V4x_2E0)))) -> ((all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0),s(A_27b,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4888 (all A_27a all F0_2E0 all F3_2E0 all F2_2E0 all F1_2E0 ((all V0P_2E0 all V1Q_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3i_2E0)))) <-> p(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))),F0_2E0),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,V3i_2E0)))))) -> ((all V2R_2E0 all V4i_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)),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V4i_2E0)))) -> ((all V2R_2E0 all V6i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V6i_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V6i_2E0)))) -> ((all V2R_2E0 all V5i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V5i_2E0)))) -> (all V0P_2E0 all V1Q_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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)),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))))))))))))) # label(thm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4889 (all A_27a all F1_2E0 all F0_2E0 ((all V1m_2E0 all V2x_2E0 all V3y_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V3y_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)),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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> ((all V1m_2E0 all V0p_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(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))),s(A_27a,V2x_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),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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(A_27a,V2x_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V2x_2E0)))))) -> (all V0p_2E0 all V1m_2E0 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),V1m_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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ALT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4890 (all A_27a all V0p_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__FORALL__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4891 (all A_27a all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4892 (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]. 7.68/7.63 4893 (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_2Eres__quan_2ERES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4894 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4895 (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]. 7.68/7.63 4896 (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]. 7.68/7.63 4897 (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]. 7.68/7.63 4898 (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]. 7.68/7.63 4899 (all A_27a all A_27b all F0_2E0 all F1_2E0 ((all V1R_2E0 all V3x_2E0 all V4i_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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0))),s(A_27b,V3x_2E0))),s(A_27a,V4i_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)),V1R_2E0),s(A_27a,V4i_2E0))),s(A_27b,V3x_2E0)))) -> ((all V1R_2E0 all V5i_2E0 ((all V6x_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,V5i_2E0))),s(A_27b,V6x_2E0))))) <-> p(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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0))),s(A_27a,V5i_2E0)))))) -> (all V0P_2E0 all V1R_2E0 all V2x_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),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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0)))))) <-> (all V3x_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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0))),s(A_27b,V3x_2E0)))))))))))) # label(thm_2Eres__quan_2ERES__FORALL__FORALL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4900 (all A_27a all F0_2E0 all F1_2E0 ((all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))) -> ((all V3x_2E0 all V4s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_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)),F1_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) -> (all V0P_2E0 all V1sos_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),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)),F1_2E0),s(A_27a,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_2Eres__quan_2ERES__EXISTS__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4901 (all A_27a all F1_2E0 all F0_2E0 ((all V1s_2E0 all V0P_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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),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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V3x_2E0)))))) -> ((all V0P_2E0 all V2x_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)),F0_2E0),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)))) -> (all V0P_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ELIM) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4902 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNION) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4903 (all A_27a all V0p_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__FORALL__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4904 (all A_27a all V0P_2E0 all V1s_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),V1s_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),V1s_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4905 (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))),c_2Epred__set_2EUNION_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),c_2Epred__set_2EUNION_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_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4906 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_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_3F_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4907 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4908 (all A_27a all A_27b all A_27c all F0_2E0 ((all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0),s(A_27b,V3x_2E0)))) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 ((exists V4y_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4909 (all A_27a all F0_2E0 all F2_2E0 all F1_2E0 ((all V1Q_2E0 all V2R_2E0 all V3i_2E0 (p(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V3i_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3i_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))))) -> ((all V2R_2E0 all V5i_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V5i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0)))) -> ((all V1Q_2E0 all V4i_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4i_2E0)))) -> (all V0P_2E0 all V1Q_2E0 all V2R_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))))))))) # label(thm_2Eres__quan_2ERES__FORALL__CONJ__DIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4910 (all A_27a all V0p_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__SELECT__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4911 (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]. 7.68/7.63 4912 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Eres__quan_2ERES__FORALL__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4913 (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]. 7.68/7.63 4914 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4915 (all A_27a all V0p_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4916 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V2t_2E0 all V0P_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,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V5x_2E0)))))) -> ((all V0P_2E0 all V4x_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) -> (all V0P_2E0 all V1s_2E0 all V2t_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4917 (all A_27a all F1_2E0 all F0_2E0 ((all V0P_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),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),V0P_2E0),s(A_27a,V3x_2E0)))))) -> ((all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V2x_2E0)))) -> (all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))))))) # label(thm_2Eres__quan_2ENOT__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4918 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V2t_2E0 all V0P_2E0 all V5x_2E0 ((-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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,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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V5x_2E0)))))) -> ((all V0P_2E0 all V4x_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) -> (all V0P_2E0 all V1s_2E0 all V2t_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))))) # label(thm_2Eres__quan_2ERES__FORALL__DIFF) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4919 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4920 (all A_27a all F0_2E0 ((all V0P_2E0 all V1f_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(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))),F0_2E0),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,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_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) -> (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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))))) # label(thm_2Eres__quan_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4921 (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))))) # label(thm_2Eres__quan_2ERES__ABSTRACT) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4922 (all A_27a all A_27b all A_27c all F0_2E0 ((all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0),s(A_27b,V3x_2E0)))) -> (all V0P_2E0 all V1s_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F0_2E0)))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__T) # label(axiom) # label(non_clause). [assumption]. 7.68/7.63 4923 (all A_27a all A_27b all F3_2E0 all F0_2E0 all F2_2E0 all F1_2E0 ((all V2R_2E0 all V3i_2E0 all V4j_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)),V2R_2E0),s(A_27a,V3i_2E0))),s(A_27b,V4j_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))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3i_2E0))),s(A_27b,V4j_2E0)))) -> ((all V1Q_2E0 all V2R_2E0 all V3i_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_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))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3i_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)),app_2E2(s(tyop_2Emin_2Efun(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_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27a,V3i_2E0)))) -> ((all V2R_2E0 all V5j_2E0 all V6i_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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27b,V5j_2E0))),s(A_27a,V6i_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)),V2R_2E0),s(A_27a,V6i_2E0))),s(A_27b,V5j_2E0)))) -> ((all V0P_2E0 all V2R_2E0 all V5j_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)),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(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27b,V5j_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),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))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))),s(A_27b,V5j_2E0)))))) -> (all V0P_2E0 all V1Q_2E0 all V2R_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),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)),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(A_27b,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_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),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(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_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))))))))))) # label(thm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4924 (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]. 7.68/7.64 4925 (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_2Eres__quan_2ERES__FORALL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4926 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4927 (all A_27a all F0_2E0 all F2_2E0 all F1_2E0 ((all V1Q_2E0 all V2R_2E0 all V3i_2E0 (p(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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V3i_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3i_2E0)))))) -> ((all V2R_2E0 all V5i_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0))),s(A_27a,V5i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0)))) -> ((all V1Q_2E0 all V4i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4i_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(A_27a,V4i_2E0)))) -> (all V0P_2E0 all V1Q_2E0 all V2R_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4928 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4929 (all A_27a all X0_2E0 all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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]. 7.68/7.64 4930 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Eres__quan_2ERES__EXISTS__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4931 (all A_27a all F1_2E0 all F0_2E0 ((all V0P_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V3x_2E0)))))) -> ((all V0P_2E0 all V2x_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)),F0_2E0),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)))) -> (all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))))))) # label(thm_2Eres__quan_2ENOT__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4932 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_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_2Epred__set_2ESUBSET_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_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4933 (all A_27a all F0_2E0 ((all V1m_2E0 all V2x_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)),F0_2E0),s(tyop_2Emin_2Ebool,V1m_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,V1m_2E0)) -> (all V0p_2E0 all V1m_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V1m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V1m_2E0)) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__FORALL__NULL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4934 (all A_27a all V0P_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Eres__quan_2ERES__FORALL__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4935 (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]. 7.68/7.64 4936 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4937 (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]. 7.68/7.64 4938 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_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))),c_2Epred__set_2EDIFF_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_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4939 (all A_27a all F0_2E0 ((all V1m_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,V1m_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)),F0_2E0),s(tyop_2Emin_2Ebool,V1m_2E0))),s(A_27a,V2x_2E0)))) -> (all V0p_2E0 all V1m_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,V1m_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V1m_2E0)))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__NULL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4940 (all A_27a all F2_2E0 all F1_2E0 all F0_2E0 ((all V0P_2E0 all V4x_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) -> ((all V0P_2E0 all V3s_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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_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)),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) -> ((all V0P_2E0 all V2x_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)),F0_2E0),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)))) -> (all V0P_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),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)),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))))) # label(thm_2Eres__quan_2ERES__EXISTS__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4941 (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]. 7.68/7.64 4942 (all A_27a all A_27b all V0r_2E0 all V1r_27_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset__r) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4943 (all A_27a all V0r1_2E0 all V1r2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__subset) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4944 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__SWAP) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4945 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__range) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4946 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4947 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_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_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_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_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_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)))) # label(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4948 (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]. 7.68/7.64 4949 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) # label(thm_2Eset__relation_2Etransitive__tc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4950 (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]. 7.68/7.64 4951 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4952 (all A_27a all V0r_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4953 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> (all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4954 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4955 (all A_27a all V0r_2E0 all V1s_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),V1s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4956 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) = s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4957 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27b_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4958 (all A_27a all X0_2E0 all 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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Epartial__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Epartial__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4959 (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_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))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(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]. 7.68/7.64 4960 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2ECURRY_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0)) # label(thm_2Eset__relation_2Ereln__to__rel__IS__CURRY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4961 (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]. 7.68/7.64 4962 (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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4963 (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]. 7.68/7.64 4964 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0),s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))) # label(thm_2Eset__relation_2Ereln__to__rel__app) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4965 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4966 (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]. 7.68/7.64 4967 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eantisym_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Eantisym_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4968 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 ((exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etc__cases__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4969 (all A_27a all V0x_2E0 all V1y_2E0 all V2r_2E0 all V3s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))))) # label(thm_2Eset__relation_2Ein__rrestrict) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4970 (all A_27a all V0s_2E0 all V1r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Eset__relation_2Edomain__rrestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4971 (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_2Eset__relation_2Erel__to__reln_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_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4972 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> (all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))))) # label(thm_2Eset__relation_2Eantisym__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4973 (all A_27a all F0_2E0 ((all V1s_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)),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2x_2E0))),s(A_27a,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)))) & s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0))) -> (all V0R_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_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_2Ebool),V1s_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)),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))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2ERREFL__EXP__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4974 (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]. 7.68/7.64 4975 (all A_27a all X0_2E0 all 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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Estrict__linear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Estrict__linear__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4976 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool))),c_2Eset__relation_2Ercomp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4977 (all A_27a all 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_2Epred__set_2EREL__RESTRICT_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_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Eset__relation_2EREL__RESTRICT__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4978 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Eset__relation_2Etc__closure) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4979 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4980 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4981 (all A_27a all A_27b all F0_2E0 ((all V0f_2E0 all V1r_2E0 all V5x_2E0 all V6y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(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))))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27a,V6y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))) -> (all V0f_2E0 all V1r_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & (all V3x_2E0 all V4y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))) -> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Eset__relation_2Efinite__prefixes__inj__image) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4982 (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]. 7.68/7.64 4983 (all A_27a all A_27c all X0_2E0 all 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))) = 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)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4984 (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]. 7.68/7.64 4985 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Estrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4986 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4987 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__subset) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4988 (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]. 7.68/7.64 4989 (all A_27a all V0r_2E0 ((all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) & (all V3x_2E0 all V4y_2E0 ((exists V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V5z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5z_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))))) # label(thm_2Eset__relation_2Etc__rules) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4990 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4991 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etc_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Etc_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Etc_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4992 (all A_27a all V0x_2E0 all V1s_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,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,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2Ein__rrestrict__alt) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4993 (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]. 7.68/7.64 4994 (all A_27a all V0r1_2E0 all V1r2_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Eset__relation_2Errestrict__union) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4995 (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]. 7.68/7.64 4996 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,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(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eset__relation_2Ercomp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4997 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0) <-> (all V2x_2E0 all V3y_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Eset__relation_2Erextension) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4998 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 4999 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Etc__SWAP) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5000 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5001 (all A_27a all A_27b all V0r_27_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))))))) # label(thm_2Eset__relation_2Edomain__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5002 (all A_27a all X0_2E0 all 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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Ereflexive_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5003 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5004 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27a,V3x_2E0) != s(A_27a,V4y_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & (all V2x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5005 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Elinear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5006 (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]. 7.68/7.64 5007 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5008 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_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_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5009 (all A_27a all V0s_2E0 all V1r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Eset__relation_2Erange__rrestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5010 (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]. 7.68/7.64 5011 (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_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5012 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5013 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5014 (all A_27a all A_27b 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_2Eset__relation_2Erel__to__reln_2E0) = 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)) # label(thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5015 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 ((exists 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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__strongind__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5016 (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(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5017 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_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_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)) # label(thm_2Eset__relation_2ERREFL__EXP__UNIV) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5018 (all A_27a all X0_2E0 s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5019 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists 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)),V1tc_27_2E0),s(A_27a,V4x_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)),V1tc_27_2E0),s(A_27a,V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__ind) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5020 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5021 (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]. 7.68/7.64 5022 (all A_27a all V0r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) # label(thm_2Eset__relation_2Esubset__tc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5023 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5024 (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_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5025 (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_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))) = 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)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5026 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists 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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__ind__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5027 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(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_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5028 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5029 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__partial__order) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5030 (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]. 7.68/7.64 5031 (all A_27a all V0s_2E0 all V1x_2E0 all V2x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2ERRUNIV_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0),s(A_27a,V2x_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Eset__relation_2ERRUNIV__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5032 (all A_27a s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Eset__relation_2Etc__empty__eqn) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5033 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5034 (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))),c_2Epred__set_2EUNION_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),c_2Epred__set_2EUNION_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_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5035 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5036 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__subset) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5037 (all A_27a all F1_2E0 all F0_2E0 ((all V1x1_2E0 all V0xs_2E0 all V2x2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) <-> p(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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))),s(A_27a,V2x2_2E0)))))) -> ((all V0xs_2E0 all V1x1_2E0 all V2x2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))),s(A_27a,V1x1_2E0))),s(A_27a,V2x2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x1_2E0),s(A_27a,V2x2_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))),s(A_27a,V2x2_2E0)))))) -> (all V0xs_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))))))) # label(thm_2Eset__relation_2Euniv__reln__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5038 (all A_27a all A_27b all V0r_2E0 all V1x_2E0 all V2x_27_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2x_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V1x_2E0),s(A_27b,V2x_27_2E0)))) # label(thm_2Eset__relation_2Ereln__to__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5039 (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(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5040 (all A_27a all V0r1_2E0 all V1r2_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))))))) # label(thm_2Eset__relation_2Etc__implication) # label(axiom) # label(non_clause). [assumption]. 7.68/7.64 5041 (all A_27a all V0x_2E0 all V1r_2E0 all V2e_2E0 all V3e_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2e_2E0),s(A_27a,V3e_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2e_2E0),s(A_27a,V3e_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(thm_2Eset__relation_2Errestrict__tc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5042 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0)))) # label(thm_2Eset__relation_2Errestrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5043 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__strongind__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5044 (all A_27a all V0r_2E0 p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) # label(thm_2Eset__relation_2Etc__transitive) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5045 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5046 (all A_27a all F1_2E0 all F0_2E0 ((all V1x_2E0 all V2y_2E0 all V0r_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0))) -> ((all V0r_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> (all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))))))) # label(thm_2Eset__relation_2Estrict__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5047 (all A_27a all V0rs_2E0 ((all V3r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0)))))) & (all V1r_2E0 all V2r_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__bigunion) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5048 (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]. 7.68/7.65 5049 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5050 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etc__domain__range) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5051 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5052 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((all V2x_2E0 all V0r1_2E0 all V3y_2E0 all V1r2_2E0 ((exists V4z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27c,V4z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,V4z_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))))) -> ((all V0r1_2E0 all V1r2_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))))) -> (all V0r1_2E0 all V1r2_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))))))) # label(thm_2Eset__relation_2Ercomp__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5053 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(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_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5054 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etc__cases) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5055 (all A_27a all X0_2E0 all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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]. 7.68/7.65 5056 (all A_27a all A_27b all V0xy_2E0 all V1R_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)),V1R_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0)))))) # label(thm_2Eset__relation_2Ein__rel__to__reln) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5057 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_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_2Epred__set_2EDISJOINT_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_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5058 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V1x_2E0 all V0r_2E0 (p(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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) <-> (exists V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))))) -> ((all V0r_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_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),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V1x_2E0)))) -> (all V0r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))))))) # label(thm_2Eset__relation_2Edomain__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5059 (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(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5060 (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_2Eset__relation_2ERRUNIV_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_2Eset__relation_2ERRUNIV_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_2Eset__relation_2ERRUNIV_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5061 (all A_27a all V0r1_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))))) -> (all V3r2_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0))))))))))) # label(thm_2Eset__relation_2Etc__union) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5062 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset__s) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5063 (all A_27a all A_27b all F1_2E0 all F0_2E0 ((all V1y_2E0 all V0r_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) -> ((all V0r_2E0 all V1y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V1y_2E0)))) -> (all V0r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) # label(thm_2Eset__relation_2Erange__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5064 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Etc_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Etc_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5065 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__linear__order) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5066 (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]. 7.68/7.65 5067 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5068 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5069 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)))))) # label(thm_2Eset__relation_2Epartial__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5070 (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]. 7.68/7.65 5071 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_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))),c_2Epred__set_2EINTER_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_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5072 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_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_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_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_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eset__relation_2ERREFL__EXP_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)))) # label(arityeq2_2Ec_2Eset__relation_2ERREFL__EXP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5073 (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]. 7.68/7.65 5074 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Eset__relation_2Eantisym__subset) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5075 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Estrict__partial__order__acyclic) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5076 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5077 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5078 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5079 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5080 (all A_27a all X0_2E0 all 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_2Epred__set_2ESUBSET_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_2Ebool,c_2Epred__set_2ESUBSET_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_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5081 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eset__relation_2Errestrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5082 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__rrestrict) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5083 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5084 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5085 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Eset__relation_2Etc__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5086 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5087 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5088 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists 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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__strongind) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5089 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Eset__relation_2Ereln__to__rel_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5090 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(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_2Ebool),X1_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5091 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Euniv__reln_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Euniv__reln_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5092 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5093 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5094 (all A_27a all V0s_2E0 all V1R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(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_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(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),V0s_2E0))))))) # label(thm_2Eset__relation_2ERREFL__EXP__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5095 (all A_27a all V0r_2E0 ((all V1x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5096 (all A_27a all V0r_2E0 all V1r_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__union) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5097 (all A_27a all A_27b all F0_2E0 ((all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),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))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,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,V1x_2E0))),s(A_27b,V2y_2E0)))))) -> (all V0R_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Eset__relation_2Erel__to__reln__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5098 (all A_27a all A_27b all F0_2E0 ((all V2e_2E0 all V0r_2E0 all V3e_27_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3e_27_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3e_27_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))),s(A_27a,V3e_27_2E0)))) -> (all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) <-> (all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))))))))))) # label(thm_2Eset__relation_2Efinite__prefixes__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5099 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,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(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5100 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(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_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))))))) # label(thm_2Eset__relation_2Ein__dom__rg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5101 (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]. 7.68/7.65 5102 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5103 (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]. 7.68/7.65 5104 (all A_27a all A_27b all A_27c all F1_2E0 all F0_2E0 ((all V3s2_2E0 all V4x_2E0 all V1r2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(A_27b,V4x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))) <-> (exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,V5y_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(A_27c,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))))))) -> ((all V3s2_2E0 all V1r2_2E0 all V4x_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))),s(A_27b,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(A_27b,V4x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))))) -> (all V0r1_2E0 all V1r2_2E0 all V2s1_2E0 all V3s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0))))))))) # label(thm_2Eset__relation_2Efinite__prefixes__comp) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5105 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5106 (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_2Ebool),c_2Epred__set_2EUNION_2E2(s(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_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(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_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Ebool))),c_2Epred__set_2EUNION_2E0),s(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_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5107 (all A_27a all V0r_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__irreflexive) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5108 (all A_27a all A_27b all V0x_2E0 all V1r_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_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0)))))) <-> (exists V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))))))) # label(thm_2Eset__relation_2Ein__domain) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5109 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etc__cases__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5110 (all A_27a all V0r_2E0 all V1tc_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),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))) & (all V3x_2E0 all V4y_2E0 ((exists 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)),V1tc_27_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5z_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V7y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Eset__relation_2Ertc__ind__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5111 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists 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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__ind__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5112 (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]. 7.68/7.65 5113 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5114 (all A_27a all F1_2E0 all F0_2E0 ((all V2x_2E0 all V3y_2E0 all V0r_2E0 all V1s_2E0 (p(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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> ((all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F1_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> (all V0r_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Eset__relation_2Errestrict__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5115 (all A_27a all V0s_2E0 all V1r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) # label(thm_2Eset__relation_2Errestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5116 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eacyclic_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Eacyclic_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5117 (all A_27a all X0_2E0 all 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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5118 (all A_27a all X0_2E0 all 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(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eirreflexive_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5119 (all A_27a all A_27b all V0y_2E0 all V1r_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_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_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(thm_2Eset__relation_2Ein__range) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5120 (all A_27a all A_27b all V0r_27_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))))))) # label(thm_2Eset__relation_2Erange__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5121 (all A_27a all V0x_2E0 all V1y_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Eset__relation_2Etc__empty) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5122 (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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5123 (all A_27a all A_27b all V0r1_2E0 all V1r2_2E0 all V2s1_2E0 all V3s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__union) # label(axiom) # label(non_clause). [assumption]. 7.68/7.65 5124 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 all V2r_27_2E0 all V3s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_27_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset__rs) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 5125 (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]. 7.68/7.66 5126 (all A_27a 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_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 5127 (all A_27a all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etc_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V1x_27_2E0)))) <-> (all V2tc_27_2E0 ((all V3a0_2E0 ((exists V6x_2E0 exists V7y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V7y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0) & (exists V8z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V8z_2E0),s(A_27a,V7y_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V8z_2E0)))))))))) | (exists V4x_2E0 exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))))) & s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V1x_27_2E0)))))))) # label(thm_2Eset__relation_2Etc__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 5128 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 5129 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Etc__idemp) # label(axiom) # label(non_clause). [assumption]. 17.24/17.19 5130 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 17.24/17.19 5131 (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]. 17.24/17.19 5132 -(all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_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_2Eset__relation_2Erel__to__reln__inv) # label(negated_conjecture) # label(non_clause). [assumption]. 17.24/17.19 17.24/17.19 ============================== end of process non-clausal formulas === 17.24/17.19 17.24/17.19 ============================== PROCESS INITIAL CLAUSES =============== 17.24/17.19 17.24/17.19 ============================== PREDICATE ELIMINATION ================= 17.24/17.19 17.24/17.19 ============================== end predicate elimination ============= 17.24/17.19 17.24/17.19 Auto_denials: (non-Horn, no changes). 17.24/17.19 17.24/17.19 Term ordering decisions: 17.24/17.19 Function symbol KB weights: tyop_2Emin_2Ebool=1. tyop_2Enum_2Enum=1. c_2Enum_2E0_2E0=1. c_2Earithmetic_2EZERO_2E0=1. c_2Elist_2ENIL_2E0=1. c_2Epred__set_2EEMPTY_2E0=1. c_2Ebool_2ET_2E0=1. c_2Ebool_2EF_2E0=1. tyop_2Eone_2Eone=1. c_2Eoption_2ENONE_2E0=1. c_2Epred__set_2EUNIV_2E0=1. c_2Ebool_2E_2F_5C_2E0=1. c_2Ebool_2E_5C_2F_2E0=1. c_2Emin_2E_3D_3D_3E_2E0=1. tyop_2Emin_2Eind=1. c_2Emin_2E_3D_2E0=1. c_2Ecombin_2Eo_2E0=1. c_2Ebool_2ECOND_2E0=1. c_2Epair_2E_2C_2E0=1. c_2Ebool_2E_7E_2E0=1. c_2Ebool_2E_21_2E0=1. c_2Ebool_2E_3F_2E0=1. combin_i_2E0=1. combin_k_2E0=1. combin_s_2E0=1. c_2Ebool_2EIN_2E0=1. c_2Epred__set_2EIMAGE_2E0=1. c_2Elist_2EMAP_2E0=1. c_2Eoption_2ESOME_2E0=1. c_2Ebool_2ELET_2E0=1. c_2Epair_2ESND_2E0=1. c_2Epair_2EFST_2E0=1. c_2Epair_2EUNCURRY_2E0=1. c_2Enum_2ESUC_2E0=1. c_2Ecombin_2EI_2E0=1. c_2Epred__set_2EGSPEC_2E0=1. c_2Ebool_2EARB_2E0=1. c_2Ecombin_2EK_2E0=1. c_2Elist_2ECONS_2E0=1. c_2Eprim__rec_2E_3C_2E0=1. c_2Epred__set_2EUNION_2E0=1. c_2Esum_2EINL_2E0=1. c_2Esum_2EINR_2E0=1. c_2Eind__type_2EBOTTOM_2E0=1. c_2Eone_2Eone_2E0=1. c_2Earithmetic_2E_2B_2E0=1. c_2Eind__type_2EZBOT_2E0=1. c_2Earithmetic_2E_3C_3D_2E0=1. c_2Epred__set_2EINSERT_2E0=1. c_2Epred__set_2ESUBSET_2E0=1. c_2Ebool_2E_3F_21_2E0=1. c_2Erelation_2EWF_2E0=1. c_2Earithmetic_2EBIT1_2E0=1. c_2Earithmetic_2EBIT2_2E0=1. c_2Earithmetic_2ENUMERAL_2E0=1. c_2Earithmetic_2E_2A_2E0=1. c_2Earithmetic_2E_2D_2E0=1. c_2Ecombin_2EC_2E0=1. c_2Elist_2ESET__TO__LIST_2E0=1. c_2Epred__set_2EINJ_2E0=1. c_2Emin_2E_40_2E0=1. c_2Enumeral_2EiDUB_2E0=1. c_2Enumeral__bit_2EiDIV2_2E0=1. c_2Epred__set_2EINTER_2E0=1. c_2Erelation_2EO_2E0=1. c_2Erelation_2Etransitive_2E0=1. c_2Ebool_2ETYPE__DEFINITION_2E0=1. c_2Epred__set_2EBIGUNION_2E0=1. c_2Earithmetic_2EDIV_2E0=1. c_2Ebool_2Eliteral__case_2E0=1. c_2Ebool_2Ethe__value_2E0=1. c_2Elist_2ELENGTH_2E0=1. c_2Elist_2ELIST__REL_2E0=1. c_2Elist_2ELIST__TO__SET_2E0=1. c_2Eoption_2EOPTION__MAP_2E0=1. c_2Epred__set_2EFINITE_2E0=1. c_2Epred__set_2EPREIMAGE_2E0=1. c_2Erelation_2EEMPTY__REL_2E0=1. c_2Erelation_2ERSUBSET_2E0=1. c_2Erelation_2ERTC_2E0=1. c_2Erelation_2ETC_2E0=1. c_2Erelation_2Einv_2E0=1. c_2Earithmetic_2EMOD_2E0=1. c_2Ebool_2EDATATYPE_2E0=1. c_2Ecombin_2ES_2E0=1. c_2Elist_2EFOLDL_2E0=1. c_2Elist_2ELIST__BIND_2E0=1. c_2Elist_2EREVERSE_2E0=1. c_2Eoption_2EOPTION__APPLY_2E0=1. c_2Eoption_2EOPTION__MCOMP_2E0=1. c_2Epred__set_2EBIJ_2E0=1. c_2Epred__set_2ECARD_2E0=1. c_2Epred__set_2ESURJ_2E0=1. c_2Erelation_2Etotal_2E0=1. c_2Earithmetic_2EEXP_2E0=1. c_2Earithmetic_2EODD_2E0=1. c_2Elist_2ELIST__APPLY_2E0=1. c_2Elist_2EZIP_2E0=1. c_2Elogroot_2ELOG_2E0=1. c_2Epred__set_2EREST_2E0=1. c_2Epred__set_2Ecountable_2E0=1. c_2Erelation_2ERUNIV_2E0=1. c_2Erelation_2Ereflexive_2E0=1. c_2Earithmetic_2EDIV2_2E0=1. c_2Earithmetic_2EFUNPOW_2E0=1. c_2Earithmetic_2EMIN_2E0=1. c_2Ebool_2ERES__EXISTS_2E0=1. c_2Ecombin_2EUPDATE_2E0=1. c_2EfixedPoint_2Efnsum_2E0=1. c_2Eind__type_2EISO_2E0=1. c_2Elist_2EAPPEND_2E0=1. c_2Elist_2EEL_2E0=1. c_2Epred__set_2EDELETE_2E0=1. c_2Epred__set_2EDIFF_2E0=1. c_2Epred__set_2EDISJOINT_2E0=1. c_2Epred__set_2ESUM__IMAGE_2E0=1. c_2Eprim__rec_2EPRE_2E0=1. c_2Eprim__rec_2Emeasure_2E0=1. c_2Erelation_2ERC_2E0=1. c_2Erelation_2EWFREC_2E0=1. c_2Erelation_2Esymmetric_2E0=1. c_2Eset__relation_2Efinite__prefixes_2E0=1. c_2Earithmetic_2EDIVMOD_2E0=1. c_2Earithmetic_2Efindq_2E0=1. c_2Ebool_2EONE__ONE_2E0=1. c_2Ebool_2ERES__ABSTRACT_2E0=1. c_2Ebool_2ERES__FORALL_2E0=1. c_2EfixedPoint_2Eempty_2E0=1. c_2Elist_2EALL__DISTINCT_2E0=1. c_2Elist_2EDROP_2E0=1. c_2Elist_2EEVERY_2E0=1. c_2Elist_2EGENLIST_2E0=1. c_2Elist_2ELUPDATE_2E0=1. c_2Elist_2EsplitAtPki_2E0=1. c_2Enum_2EZERO__REP_2E0=1. c_2Enumpair_2Enlistrec_2E0=1. c_2Eoption_2EOPTION__BIND_2E0=1. c_2Eoption_2ETHE_2E0=1. c_2Eoption_2Eoption__CASE_2E0=1. c_2Epair_2ESWAP_2E0=1. c_2Epred__set_2EBIGINTER_2E0=1. c_2Epred__set_2ECROSS_2E0=1. c_2Erelation_2ERUNION_2E0=1. c_2Erelation_2Einv__image_2E0=1. c_2Ewhile_2ELEAST_2E0=1. c_2Earithmetic_2EEVEN_2E0=1. c_2Earithmetic_2EFACT_2E0=1. c_2Earithmetic_2EMAX_2E0=1. c_2Earithmetic_2E_3E_3D_2E0=1. c_2Ebit_2EBITWISE_2E0=1. c_2Ebit_2ELOG2_2E0=1. c_2Ebit_2EMOD__2EXP_2E0=1. c_2Ebool_2EONTO_2E0=1. c_2Ebool_2ERES__EXISTS__UNIQUE_2E0=1. c_2Ecombin_2EASSOC_2E0=1. c_2Edivides_2Edivides_2E0=1. c_2Elist_2EFLAT_2E0=1. c_2Elist_2EFOLDR_2E0=1. c_2Elist_2EMAP2_2E0=1. c_2Elist_2ESNOC_2E0=1. c_2Elist_2ETAKE_2E0=1. c_2Elist_2Elist__CASE_2E0=1. c_2Emarker_2EAbbrev_2E0=1. c_2Eoption_2EIS__SOME_2E0=1. c_2Eoption_2EOPTION__IGNORE__BIND_2E0=1. c_2Epair_2ECURRY_2E0=1. c_2Eposet_2Efunction_2E0=1. c_2Epred__set_2ECOMPL_2E0=1. c_2Epred__set_2EFUNSET_2E0=1. c_2Epred__set_2EITSET_2E0=1. c_2Epred__set_2EMIN__SET_2E0=1. c_2Epred__set_2EREL__RESTRICT_2E0=1. c_2Epred__set_2Ecount_2E0=1. c_2Erelation_2EINVOL_2E0=1. c_2Erelation_2ERINTER_2E0=1. c_2Erelation_2ESC_2E0=1. c_2Erelation_2ESTRORD_2E0=1. c_2Erelation_2EStrongOrder_2E0=1. c_2Erelation_2EWeakOrder_2E0=1. c_2Erelation_2Eantisymmetric_2E0=1. c_2Erelation_2Eirreflexive_2E0=1. c_2Eset__relation_2Erange_2E0=1. c_2Eset__relation_2Ereln__to__rel_2E0=1. c_2Ewhile_2EWHILE_2E0=1. c_2Earithmetic_2EABS__DIFF_2E0=1. c_2Earithmetic_2ENRC_2E0=1. c_2Earithmetic_2E_3E_2E0=1. c_2Ebit_2EBIT_2E0=1. c_2Ebit_2EBIT__MODIFY_2E0=1. c_2Ebit_2EBIT__REVERSE_2E0=1. c_2Ebit_2EDIV__2EXP_2E0=1. c_2Ebit_2ELOWEST__SET__BIT_2E0=1. c_2Ebit_2EMOD__2EXP__EQ_2E0=1. c_2Ebit_2EMOD__2EXP__MAX_2E0=1. c_2Ebit_2ESBIT_2E0=1. c_2Ebit_2ETIMES__2EXP_2E0=1. c_2Ebool_2ERES__SELECT_2E0=1. c_2Ecombin_2ECOMM_2E0=1. c_2Ecombin_2EFAIL_2E0=1. c_2Ecombin_2EFCOMM_2E0=1. c_2Ecombin_2ELEFT__ID_2E0=1. c_2Ecombin_2EMONOID_2E0=1. c_2Ecombin_2ERIGHT__ID_2E0=1. c_2Edivides_2Eprime_2E0=1. c_2EfixedPoint_2Emonotone_2E0=1. c_2Egcd_2Egcd_2E0=1. c_2Eind__type_2ECONSTR_2E0=1. c_2Eind__type_2EFCONS_2E0=1. c_2Eind__type_2EINJA_2E0=1. c_2Eind__type_2EINJF_2E0=1. c_2Eind__type_2EINJN_2E0=1. c_2Eind__type_2EINJP_2E0=1. c_2Eind__type_2EZRECSPACE_2E0=1. c_2Elist_2EEXISTS_2E0=1. c_2Elist_2EFOLDL2_2E0=1. c_2Elist_2EHD_2E0=1. c_2Elist_2EINDEX__FIND_2E0=1. c_2Elist_2ELAST_2E0=1. c_2Elist_2ELLEX_2E0=1. c_2Elist_2EOPT__MMAP_2E0=1. c_2Elist_2ESHORTLEX_2E0=1. c_2Elist_2ETL_2E0=1. c_2Elist_2EdropWhile_2E0=1. c_2Elist_2EoHD_2E0=1. c_2Emarker_2Estmarker_2E0=1. c_2Enum_2EIS__NUM__REP_2E0=1. c_2Enum_2ESUC__REP_2E0=1. c_2Enumeral_2EiBIT__cases_2E0=1. c_2Enumeral_2Einternal__mult_2E0=1. c_2Enumeral__bit_2EFDUB_2E0=1. c_2Enumeral__bit_2EiBITWISE_2E0=1. c_2Enumeral__bit_2EiMOD__2EXP_2E0=1. c_2Enumeral__bit_2EiSUC_2E0=1. c_2Enumpair_2Enfst_2E0=1. c_2Enumpair_2Enlen_2E0=1. c_2Enumpair_2Enmap_2E0=1. c_2Enumpair_2Enpair_2E0=1. c_2Enumpair_2Ensnd_2E0=1. c_2Eoption_2EOPTION__MAP2_2E0=1. c_2Eoption_2EOPTREL_2E0=1. c_2Epair_2ELEX_2E0=1. c_2Epair_2E_23_23_2E0=1. c_2Eposet_2Ecomplete_2E0=1. c_2Eposet_2Epointwise__lift_2E0=1. c_2Epred__set_2ECHOICE_2E0=1. c_2Epred__set_2EDFUNSET_2E0=1. c_2Epred__set_2ELINV_2E0=1. c_2Epred__set_2ELINV__OPT_2E0=1. c_2Epred__set_2EMAX__SET_2E0=1. c_2Epred__set_2EPROD__IMAGE_2E0=1. c_2Epred__set_2EPROD__SET_2E0=1. c_2Epred__set_2ESUM__SET_2E0=1. c_2Epred__set_2Eschroeder__close_2E0=1. c_2Eprim__rec_2EPRIM__REC__FUN_2E0=1. c_2Eprim__rec_2ESIMP__REC_2E0=1. c_2Erelation_2EEQC_2E0=1. c_2Erelation_2EIDEM_2E0=1. c_2Erelation_2EOrder_2E0=1. c_2Erelation_2ERCOMPL_2E0=1. c_2Erelation_2ERDOM_2E0=1. c_2Erelation_2ERDOM__DELETE_2E0=1. c_2Erelation_2ERESTRICT_2E0=1. c_2Erelation_2ERRANGE_2E0=1. c_2Erelation_2ERRESTRICT_2E0=1. c_2Erelation_2Ediag_2E0=1. c_2Eset__relation_2Edomain_2E0=1. c_2Eset__relation_2Ercomp_2E0=1. c_2Eset__relation_2Erel__to__reln_2E0=1. c_2Eset__relation_2Etc_2E0=1. c_2Esum_2EIS__SUM__REP_2E0=1. c_2Esum_2E_2B_2B_2E0=1. c_2Esum_2Esum__CASE_2E0=1. c_2Ewhile_2EHOARE__SPEC_2E0=1. c_2Ewhile_2EOLEAST_2E0=1. c_2EConseqConv_2EASM__MARKER_2E0=1. c_2Earithmetic_2EMODEQ_2E0=1. c_2Earithmetic_2Enat__elim____magic_2E0=1. c_2Earithmetic_2Enum__CASE_2E0=1. c_2EbasicSize_2Ebool__size_2E0=1. c_2EbasicSize_2Eone__size_2E0=1. c_2EbasicSize_2Eoption__size_2E0=1. c_2EbasicSize_2Epair__size_2E0=1. c_2EbasicSize_2Esum__size_2E0=1. c_2Ebit_2EBITS_2E0=1. c_2Ebit_2EBITV_2E0=1. c_2Ebit_2EDIVMOD__2EXP_2E0=1. c_2Ebit_2ESIGN__EXTEND_2E0=1. c_2Ebit_2ESLICE_2E0=1. c_2Ebool_2EBOUNDED_2E0=1. c_2Ebool_2Eitself__case_2E0=1. c_2Ecombin_2EW_2E0=1. c_2Ecombin_2E_3A_3E_2E0=1. c_2Edivides_2EPRIMES_2E0=1. c_2EfixedPoint_2Eclosed_2E0=1. c_2EfixedPoint_2Edense_2E0=1. c_2EfixedPoint_2Egfp_2E0=1. c_2EfixedPoint_2Elfp_2E0=1. c_2Egcd_2Eis__gcd_2E0=1. c_2Egcd_2Elcm_2E0=1. c_2Egcdset_2Egcdset_2E0=1. c_2Eind__type_2EFNIL_2E0=1. c_2Eind__type_2ENUMFST_2E0=1. c_2Eind__type_2ENUMLEFT_2E0=1. c_2Eind__type_2ENUMPAIR_2E0=1. c_2Eind__type_2ENUMRIGHT_2E0=1. c_2Eind__type_2ENUMSND_2E0=1. c_2Eind__type_2ENUMSUM_2E0=1. c_2Eind__type_2EZCONSTR_2E0=1. c_2Eind__type_2Edest__rec_2E0=1. c_2Eind__type_2Emk__rec_2E0=1. c_2Elist_2EEVERYi_2E0=1. c_2Elist_2EFILTER_2E0=1. c_2Elist_2EFIND_2E0=1. c_2Elist_2EFRONT_2E0=1. c_2Elist_2EGENLIST__AUX_2E0=1. c_2Elist_2EINDEX__OF_2E0=1. c_2Elist_2ELEN_2E0=1. c_2Elist_2ELIST__GUARD_2E0=1. c_2Elist_2ELIST__IGNORE__BIND_2E0=1. c_2Elist_2ELIST__LIFT2_2E0=1. c_2Elist_2ELRC_2E0=1. c_2Elist_2ENULL_2E0=1. c_2Elist_2EPAD__LEFT_2E0=1. c_2Elist_2EPAD__RIGHT_2E0=1. c_2Elist_2EREV_2E0=1. c_2Elist_2ESUM_2E0=1. c_2Elist_2ESUM__ACC_2E0=1. c_2Elist_2EUNIQUE_2E0=1. c_2Elist_2EUNZIP_2E0=1. c_2Elist_2EisPREFIX_2E0=1. c_2Elist_2Elist__size_2E0=1. c_2Elist_2Enub_2E0=1. c_2Elist_2EoEL_2E0=1. c_2Elogroot_2EROOT_2E0=1. c_2Elogroot_2ESQRTd_2E0=1. c_2Elogroot_2EiSQRT0_2E0=1. c_2Elogroot_2EiSQRT1_2E0=1. c_2Elogroot_2EiSQRT2_2E0=1. c_2Elogroot_2EiSQRT3_2E0=1. c_2Emarker_2EAC_2E0=1. c_2Emarker_2ECong_2E0=1. c_2Emarker_2EIfCases_2E0=1. c_2Emarker_2E_3A_2D_2E0=1. c_2Emarker_2Eunint_2E0=1. c_2EnormalForms_2EEXT__POINT_2E0=1. c_2EnormalForms_2EUNIV__POINT_2E0=1. c_2Enum_2EABS__num_2E0=1. c_2Enum_2EREP__num_2E0=1. c_2Enumeral_2Eexactlog_2E0=1. c_2Enumeral_2EiSQR_2E0=1. c_2Enumeral_2EiSUB_2E0=1. c_2Enumeral_2EiZ_2E0=1. c_2Enumeral_2EiiSUC_2E0=1. c_2Enumeral_2Eonecount_2E0=1. c_2Enumeral_2Etexp__help_2E0=1. c_2Enumeral__bit_2EBIT__MODF_2E0=1. c_2Enumeral__bit_2EBIT__REV_2E0=1. c_2Enumeral__bit_2ESFUNPOW_2E0=1. c_2Enumeral__bit_2EiLOG2_2E0=1. c_2Enumpair_2Einvtri0_2E0=1. c_2Enumpair_2Einvtri_2E0=1. c_2Enumpair_2Enapp_2E0=1. c_2Enumpair_2Encons_2E0=1. c_2Enumpair_2Enfoldl_2E0=1. c_2Enumpair_2Etri_2E0=1. c_2Eone_2Eone__CASE_2E0=1. c_2Eoption_2EIS__NONE_2E0=1. c_2Eoption_2EOPTION__ALL_2E0=1. c_2Eoption_2EOPTION__CHOICE_2E0=1. c_2Eoption_2EOPTION__GUARD_2E0=1. c_2Eoption_2EOPTION__JOIN_2E0=1. c_2Eoption_2Eoption__ABS_2E0=1. c_2Eoption_2Eoption__REP_2E0=1. c_2Eoption_2Esome_2E0=1. c_2Epair_2EABS__prod_2E0=1. c_2Epair_2EPROD__ALL_2E0=1. c_2Epair_2EREP__prod_2E0=1. c_2Epair_2ERPROD_2E0=1. c_2Epair_2Epair__CASE_2E0=1. c_2Eposet_2Ebottom_2E0=1. c_2Eposet_2Ecarrier_2E0=1. c_2Eposet_2Echain_2E0=1. c_2Eposet_2Econtinuous_2E0=1. c_2Eposet_2Edown__continuous_2E0=1. c_2Eposet_2Egfp_2E0=1. c_2Eposet_2Eglb_2E0=1. c_2Eposet_2Elfp_2E0=1. c_2Eposet_2Elub_2E0=1. c_2Eposet_2Emonotonic_2E0=1. c_2Eposet_2Eposet_2E0=1. c_2Eposet_2Erelation_2E0=1. c_2Eposet_2Etop_2E0=1. c_2Eposet_2Eup__continuous_2E0=1. c_2Epred__set_2EPOW_2E0=1. c_2Epred__set_2EPSUBSET_2E0=1. c_2Epred__set_2ERINV_2E0=1. c_2Epred__set_2ESING_2E0=1. c_2Epred__set_2Echooser_2E0=1. c_2Epred__set_2Eenumerate_2E0=1. c_2Epred__set_2Eequiv__on_2E0=1. c_2Epred__set_2Eis__measure__maximal_2E0=1. c_2Epred__set_2Enum__to__pair_2E0=1. c_2Epred__set_2Epair__to__num_2E0=1. c_2Epred__set_2Epairwise_2E0=1. c_2Epred__set_2Epartition_2E0=1. c_2Eprim__rec_2EPRIM__REC_2E0=1. c_2Eprim__rec_2ESIMP__REC__REL_2E0=1. c_2Eprim__rec_2Ewellfounded_2E0=1. c_2Erelation_2ECR_2E0=1. c_2Erelation_2EINDUCTIVE__INVARIANT_2E0=1. c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E0=1. c_2Erelation_2ELinearOrder_2E0=1. c_2Erelation_2EPreOrder_2E0=1. c_2Erelation_2ESN_2E0=1. c_2Erelation_2EStrongLinearOrder_2E0=1. c_2Erelation_2EWCR_2E0=1. c_2Erelation_2EWFP_2E0=1. c_2Erelation_2EWeakLinearOrder_2E0=1. c_2Erelation_2Eapprox_2E0=1. c_2Erelation_2Ediamond_2E0=1. c_2Erelation_2Eequivalence_2E0=1. c_2Erelation_2Enf_2E0=1. c_2Erelation_2Ercdiamond_2E0=1. c_2Erelation_2Ethe__fun_2E0=1. c_2Erelation_2Etrichotomous_2E0=1. c_2Eset__relation_2ERREFL__EXP_2E0=1. c_2Eset__relation_2ERRUNIV_2E0=1. c_2Eset__relation_2Eacyclic_2E0=1. c_2Eset__relation_2Eantisym_2E0=1. c_2Eset__relation_2Eirreflexive_2E0=1. c_2Eset__relation_2Elinear__order_2E0=1. c_2Eset__relation_2Epartial__order_2E0=1. c_2Eset__relation_2Ereflexive_2E0=1. c_2Eset__relation_2Errestrict_2E0=1. c_2Eset__relation_2Estrict_2E0=1. c_2Eset__relation_2Estrict__linear__order_2E0=1. c_2Eset__relation_2Etransitive_2E0=1. c_2Eset__relation_2Euniv__reln_2E0=1. c_2Esum_2EABS__sum_2E0=1. c_2Esum_2EISL_2E0=1. c_2Esum_2EISR_2E0=1. c_2Esum_2EOUTL_2E0=1. c_2Esum_2EOUTR_2E0=1. c_2Esum_2EREP__sum_2E0=1. c_2Esum_2ESUM__ALL_2E0=1. c_2Ewhile_2EOWHILE_2E0=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. s=1. tyop_2Emin_2Efun=1. app_2E2=1. tyop_2Epair_2Eprod=1. c_2Ebool_2EIN_2E2=1. c_2Epair_2E_2C_2E2=1. c_2Eprim__rec_2E_3C_2E2=1. tyop_2Esum_2Esum=1. c_2Earithmetic_2E_2B_2E2=1. c_2Elist_2ECONS_2E2=1. c_2Earithmetic_2E_3C_3D_2E2=1. c_2Earithmetic_2E_2A_2E2=1. c_2Earithmetic_2E_2D_2E2=1. c_2Earithmetic_2EEXP_2E2=1. c_2Epred__set_2ESUBSET_2E2=1. c_2Elist_2EAPPEND_2E2=1. c_2Earithmetic_2EMOD_2E2=1. c_2Epred__set_2EINSERT_2E2=1. c_2Ebool_2ERES__FORALL_2E2=1. c_2Elist_2EMAP_2E2=1. c_2Epred__set_2EIMAGE_2E2=1. c_2Epred__set_2EUNION_2E2=1. c_2Ebool_2ERES__EXISTS_2E2=1. c_2Ecombin_2Eo_2E2=1. c_2Ebit_2EBIT_2E2=1. c_2Elist_2EEVERY_2E2=1. c_2Earithmetic_2EDIV_2E2=1. c_2Elist_2EEL_2E2=1. c_2Epred__set_2EINTER_2E2=1. c_2Ebool_2ELET_2E2=1. c_2Ebool_2E_2F_5C_2E2=1. c_2Ebool_2E_5C_2F_2E2=1. c_2Emin_2E_3D_3D_3E_2E2=1. c_2Epred__set_2EDISJOINT_2E2=1. c_2Edivides_2Edivides_2E2=1. c_2Epred__set_2EDIFF_2E2=1. c_2Epred__set_2EDELETE_2E2=1. c_2Egcd_2Egcd_2E2=1. c_2Elist_2EFILTER_2E2=1. c_2Elist_2EGENLIST_2E2=1. c_2Emin_2E_3D_2E2=1. c_2Ebool_2ERES__EXISTS__UNIQUE_2E2=1. c_2Epred__set_2ECROSS_2E2=1. c_2Epred__set_2ESUM__IMAGE_2E2=1. c_2Elist_2EEXISTS_2E2=1. c_2Elist_2ESNOC_2E2=1. c_2Elist_2ETAKE_2E2=1. c_2Ebool_2ETYPE__DEFINITION_2E2=1. c_2Elist_2EDROP_2E2=1. c_2Epred__set_2Eequiv__on_2E2=1. c_2Earithmetic_2EMIN_2E2=1. c_2Earithmetic_2EMAX_2E2=1. c_2Enumeral_2Etexp__help_2E2=1. c_2Epred__set_2EPREIMAGE_2E2=1. c_2Eset__relation_2Efinite__prefixes_2E2=1. c_2Elogroot_2ELOG_2E2=1. c_2Earithmetic_2EABS__DIFF_2E2=1. c_2Erelation_2ERSUBSET_2E2=1. c_2Eset__relation_2Errestrict_2E2=1. c_2Eoption_2EOPTION__MAP_2E2=1. c_2Earithmetic_2E_3E_2E2=1. c_2Elist_2ELIST__BIND_2E2=1. c_2Elist_2EisPREFIX_2E2=1. c_2Enumeral_2Einternal__mult_2E2=1. c_2Epred__set_2EPSUBSET_2E2=1. c_2Ebool_2Eliteral__case_2E2=1. c_2Eposet_2Echain_2E2=1. c_2Epred__set_2EFUNSET_2E2=1. c_2Earithmetic_2E_3E_3D_2E2=1. c_2Eoption_2EOPTION__BIND_2E2=1. c_2Epred__set_2Epairwise_2E2=1. c_2Erelation_2EWFP_2E2=1. c_2Erelation_2EWFREC_2E2=1. c_2Ebool_2ERES__ABSTRACT_2E2=1. c_2Erelation_2EO_2E2=1. c_2Elist_2EoEL_2E2=1. c_2Enumpair_2Encons_2E2=1. c_2Eposet_2Edown__continuous_2E2=1. c_2Eposet_2Eup__continuous_2E2=1. c_2Ewhile_2EWHILE_2E2=1. c_2Eind__type_2EISO_2E2=1. c_2Enumeral__bit_2EFDUB_2E2=1. c_2Eoption_2EOPTION__APPLY_2E2=1. c_2Epred__set_2Epartition_2E2=1. c_2Ebit_2ESBIT_2E2=1. c_2Ebool_2ERES__SELECT_2E2=1. c_2Elist_2ELIST__APPLY_2E2=1. c_2Eset__relation_2Epartial__order_2E2=1. c_2Elogroot_2EROOT_2E2=1. c_2Erelation_2ERUNION_2E2=1. c_2Ebit_2EMOD__2EXP_2E2=1. c_2Egcd_2Elcm_2E2=1. c_2Enumpair_2Enpair_2E2=1. c_2Eset__relation_2Elinear__order_2E2=1. c_2Ecombin_2EC_2E2=1. c_2EfixedPoint_2Efnsum_2E2=1. c_2Elist_2EdropWhile_2E2=1. c_2Epair_2EUNCURRY_2E2=1. c_2Eind__type_2ENUMPAIR_2E2=1. c_2Enumeral__bit_2EiMOD__2EXP_2E2=1. c_2Eoption_2EOPTION__IGNORE__BIND_2E2=1. c_2Eoption_2EOPTION__MCOMP_2E2=1. c_2Epair_2ELEX_2E2=1. c_2Erelation_2ERINTER_2E2=1. c_2Eset__relation_2Estrict__linear__order_2E2=1. c_2Eoption_2EOPTION__ALL_2E2=1. c_2Epair_2Epair__CASE_2E2=1. c_2Eset__relation_2Etc_2E2=1. c_2Ebit_2EMOD__2EXP__MAX_2E2=1. c_2Eind__type_2EINJP_2E2=1. c_2Eind__type_2ENUMSUM_2E2=1. c_2Elist_2EOPT__MMAP_2E2=1. c_2Eposet_2Emonotonic_2E2=1. c_2Epred__set_2EREL__RESTRICT_2E2=1. c_2Ebit_2EBIT__REVERSE_2E2=1. c_2Ecombin_2ES_2E2=1. c_2Elist_2EEVERYi_2E2=1. c_2Enumeral_2Eonecount_2E2=1. c_2Epred__set_2Echooser_2E2=1. c_2Ebit_2EDIV__2EXP_2E2=1. c_2Ecombin_2EMONOID_2E2=1. c_2Elist_2Elist__size_2E2=1. c_2Enumpair_2Einvtri0_2E2=1. c_2Eset__relation_2Ercomp_2E2=1. c_2Ecombin_2EFAIL_2E2=1. c_2Elist_2ELIST__TO__SET_2E2=1. c_2Elist_2EUNIQUE_2E2=1. c_2EnormalForms_2EEXT__POINT_2E2=1. c_2Eoption_2EOPTION__CHOICE_2E2=1. c_2Epred__set_2Eschroeder__close_2E2=1. c_2Erelation_2Einv__image_2E2=1. c_2Ecombin_2ELEFT__ID_2E2=1. c_2Ecombin_2ERIGHT__ID_2E2=1. c_2Elist_2ELEN_2E2=1. c_2Elist_2EREV_2E2=1. c_2Elist_2ESUM__ACC_2E2=1. c_2Eposet_2Ebottom_2E2=1. c_2Eposet_2Epointwise__lift_2E2=1. c_2Eposet_2Etop_2E2=1. c_2Eset__relation_2ERREFL__EXP_2E2=1. c_2Eset__relation_2Ereflexive_2E2=1. c_2Ebit_2ETIMES__2EXP_2E2=1. c_2Ecombin_2EFCOMM_2E2=1. c_2Enumpair_2Enapp_2E2=1. c_2Epair_2ERPROD_2E2=1. c_2Epred__set_2EDFUNSET_2E2=1. c_2Epred__set_2EPROD__IMAGE_2E2=1. c_2EfixedPoint_2Eclosed_2E2=1. c_2EfixedPoint_2Edense_2E2=1. c_2Emarker_2EAC_2E2=1. c_2Enumpair_2Enmap_2E2=1. c_2Eposet_2Econtinuous_2E2=1. c_2Eposet_2Efunction_2E2=1. c_2Epred__set_2EBIGINTER_2E2=1. c_2Epred__set_2EBIGUNION_2E2=1. c_2Erelation_2ERRESTRICT_2E2=1. c_2EConseqConv_2EASM__MARKER_2E2=1. c_2EbasicSize_2Eoption__size_2E2=1. c_2Ebit_2EBITV_2E2=1. c_2Ebit_2EDIVMOD__2EXP_2E2=1. c_2Ecombin_2EK_2E2=1. c_2Ecombin_2EW_2E2=1. c_2Eind__type_2EFCONS_2E2=1. c_2Elist_2EINDEX__FIND_2E2=1. c_2Enumpair_2Enlistrec_2E2=1. c_2Eone_2Eone__CASE_2E2=1. c_2Epred__set_2EGSPEC_2E2=1. c_2Epred__set_2EREST_2E2=1. c_2Erelation_2ERDOM_2E2=1. c_2Erelation_2ERDOM__DELETE_2E2=1. c_2Erelation_2ERRANGE_2E2=1. c_2Eset__relation_2Eirreflexive_2E2=1. c_2EbasicSize_2Epair__size_2E2=1. c_2Ebool_2Eitself__case_2E2=1. c_2Ecombin_2E_3A_3E_2E2=1. c_2Eind__type_2EINJF_2E2=1. c_2Elist_2ELIST__IGNORE__BIND_2E2=1. c_2Elist_2EsplitAtPki_2E2=1. c_2Emarker_2E_3A_2D_2E2=1. c_2Epred__set_2ECOMPL_2E2=1. c_2Epred__set_2ELINV_2E2=1. c_2Epred__set_2ELINV__OPT_2E2=1. c_2Epred__set_2Ecount_2E2=1. c_2Eprim__rec_2EPRIM__REC__FUN_2E2=1. c_2Eprim__rec_2ESIMP__REC_2E2=1. c_2Erelation_2EEMPTY__REL_2E2=1. c_2Erelation_2ERUNIV_2E2=1. c_2Erelation_2Enf_2E2=1. c_2Esum_2E_2B_2B_2E2=1. f1=1. f3=1. f8=1. f9=1. f10=1. f18=1. f19=1. f21=1. f22=1. f23=1. f43=1. f44=1. f55=1. f74=1. f75=1. f76=1. f77=1. f78=1. f84=1. f85=1. f91=1. f95=1. f96=1. f100=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f157=1. f158=1. f159=1. f160=1. f164=1. f173=1. f174=1. f175=1. f201=1. f202=1. f209=1. f210=1. f211=1. f214=1. f215=1. f216=1. f222=1. f223=1. f231=1. f232=1. f233=1. f235=1. f236=1. f237=1. f240=1. f241=1. f250=1. f254=1. f255=1. f256=1. f257=1. f258=1. f259=1. f260=1. f272=1. f275=1. f276=1. f280=1. f281=1. f284=1. f286=1. f287=1. f294=1. f295=1. f315=1. f316=1. f331=1. f332=1. f341=1. f346=1. f374=1. f375=1. f394=1. f395=1. f421=1. f435=1. f441=1. f442=1. f443=1. f450=1. f457=1. f458=1. f459=1. f465=1. f466=1. f468=1. f470=1. f472=1. f473=1. f478=1. f479=1. f491=1. f493=1. f500=1. f501=1. f502=1. f505=1. f506=1. f507=1. f511=1. f523=1. f536=1. f548=1. f550=1. f551=1. f558=1. f561=1. f562=1. f574=1. f575=1. f577=1. f588=1. f589=1. f591=1. f592=1. f595=1. f596=1. f606=1. f712=1. f718=1. f719=1. f720=1. f721=1. f722=1. f723=1. f730=1. f738=1. f739=1. f740=1. f741=1. f744=1. f745=1. f746=1. f747=1. f748=1. f749=1. f750=1. f751=1. f760=1. f768=1. f769=1. f770=1. f777=1. f780=1. f781=1. f782=1. f783=1. f784=1. f785=1. f788=1. f790=1. f809=1. f813=1. f814=1. f815=1. f816=1. f817=1. f821=1. f822=1. f823=1. f824=1. f827=1. f829=1. f832=1. f841=1. f845=1. f846=1. f863=1. f868=1. f869=1. f870=1. f871=1. f875=1. f883=1. f884=1. f885=1. f896=1. f897=1. f898=1. f903=1. f904=1. f905=1. f906=1. f907=1. f908=1. f909=1. f914=1. f915=1. f921=1. f922=1. f923=1. f924=1. f925=1. f929=1. f938=1. f957=1. f958=1. f959=1. f977=1. f978=1. f979=1. f980=1. f981=1. f994=1. f996=1. f1009=1. f1010=1. f1011=1. f1012=1. f1015=1. f1016=1. f1023=1. f1029=1. f1031=1. f1033=1. f1034=1. f1035=1. f1042=1. f1045=1. f1050=1. f1051=1. f1052=1. f1053=1. f1054=1. f1055=1. f1056=1. f1057=1. f1058=1. f1059=1. f1065=1. f1066=1. f1067=1. f1072=1. f1074=1. f1081=1. f1083=1. f1084=1. f1085=1. f1098=1. f1099=1. f1100=1. f1111=1. f1114=1. f1115=1. f1119=1. f1129=1. f1130=1. f1153=1. f1154=1. f1155=1. f1160=1. f1169=1. f1182=1. f1185=1. f1186=1. f1187=1. f1188=1. f1189=1. f1190=1. f1191=1. f1193=1. f1195=1. f1200=1. f1203=1. f1204=1. f1206=1. f1207=1. f1208=1. f1209=1. f1210=1. f1211=1. f1212=1. f1213=1. f1217=1. f1218=1. f1220=1. f1222=1. f1224=1. f1225=1. f1226=1. f1230=1. f1231=1. f1233=1. f1234=1. f1235=1. f1237=1. f1238=1. f1241=1. f1247=1. f1248=1. f1250=1. f1251=1. f1276=1. f1277=1. f1280=1. f1289=1. f1290=1. f1291=1. f1292=1. f1294=1. f1295=1. f1296=1. f1299=1. f1306=1. f1307=1. f1321=1. f1322=1. f1330=1. f1333=1. f1350=1. f1351=1. f1355=1. f1358=1. f1382=1. f1385=1. f1390=1. f1391=1. f1394=1. f1398=1. f1419=1. f1430=1. f1431=1. f1436=1. f1437=1. f1438=1. f1444=1. f1448=1. f1449=1. f1455=1. f1456=1. f1457=1. f1458=1. f1471=1. f1472=1. f1473=1. f1474=1. f1475=1. f1489=1. f1490=1. f1501=1. f1506=1. f1507=1. f1508=1. f1521=1. f1531=1. f1533=1. f1534=1. f1535=1. f1544=1. f1545=1. f1546=1. f1549=1. f1559=1. f1565=1. f1576=1. f1583=1. f1584=1. f1588=1. f1589=1. f1590=1. f1591=1. f1592=1. f1594=1. f1603=1. f1627=1. f1628=1. f1629=1. f1630=1. f1631=1. f1632=1. f1633=1. f1634=1. f1637=1. f1638=1. f1639=1. f1665=1. f1666=1. f1667=1. f1668=1. f1677=1. f1678=1. f1679=1. f1692=1. f1700=1. f1701=1. f1702=1. f1703=1. f1707=1. f1708=1. f1710=1. f1711=1. f1712=1. f1729=1. f1730=1. f1732=1. f1733=1. f1754=1. f1755=1. f1760=1. f1793=1. f1794=1. f1795=1. f1815=1. f1816=1. f1824=1. f1825=1. f1826=1. f1827=1. f1828=1. f1835=1. f1838=1. f1839=1. f1840=1. f1842=1. f1843=1. f1844=1. f1845=1. f1846=1. f1847=1. f1848=1. f1849=1. f1861=1. f1862=1. f1863=1. f1870=1. f1874=1. f1875=1. f1876=1. f1877=1. f1878=1. f1879=1. f1883=1. f1884=1. f1912=1. f1913=1. f1914=1. f1915=1. f1917=1. f1918=1. f1919=1. f1920=1. f1926=1. f1927=1. f1928=1. f1929=1. f1945=1. f1948=1. f1949=1. f1950=1. f1964=1. f1965=1. f1968=1. f1969=1. f1970=1. f1971=1. f1972=1. f1973=1. f1974=1. f1977=1. f1978=1. f1981=1. f1982=1. f1983=1. f2005=1. f2009=1. f2010=1. f2011=1. f2012=1. f2013=1. f2014=1. f2015=1. f2016=1. f2017=1. f2029=1. f2030=1. f2033=1. f2047=1. f2048=1. f2051=1. f2052=1. f2063=1. f2064=1. f2066=1. f2076=1. f2077=1. f2137=1. f2138=1. f2139=1. f2165=1. f2166=1. f2167=1. f2168=1. f2169=1. f2176=1. f2177=1. f2178=1. f2180=1. f2183=1. f2184=1. f2185=1. f2186=1. f2187=1. f2194=1. f2234=1. f2235=1. f2236=1. f2264=1. tyop_2Elist_2Elist=1. tyop_2Eoption_2Eoption=1. c_2Earithmetic_2ENUMERAL_2E1=1. c_2Earithmetic_2EBIT1_2E1=1. c_2Earithmetic_2EBIT2_2E1=1. c_2Enum_2ESUC_2E1=1. c_2Elist_2ELENGTH_2E1=1. c_2Epred__set_2EFINITE_2E1=1. tyop_2Eind__type_2Erecspace=1. c_2Eoption_2ESOME_2E1=1. c_2Elist_2ELIST__TO__SET_2E1=1. c_2Epred__set_2EGSPEC_2E1=1. c_2Epred__set_2ECARD_2E1=1. c_2Ebool_2E_3F_2E1=1. c_2Ebool_2E_21_2E1=1. c_2Eset__relation_2Etc_2E1=1. c_2Epair_2EUNCURRY_2E1=1. c_2Erelation_2EWF_2E1=1. c_2Epred__set_2EBIGUNION_2E1=1. c_2Earithmetic_2EODD_2E1=1. c_2Epred__set_2Ecountable_2E1=1. c_2Eprim__rec_2EPRE_2E1=1. c_2Epair_2EFST_2E1=1. c_2Epair_2ESND_2E1=1. c_2Eposet_2Eposet_2E1=1. c_2Elist_2EALL__DISTINCT_2E1=1. c_2Ebool_2E_3F_21_2E1=1. c_2Emin_2E_40_2E1=1. c_2Esum_2EINL_2E1=1. c_2Esum_2EINR_2E1=1. c_2Erelation_2Etransitive_2E1=1. c_2Elist_2EZIP_2E1=1. c_2Enumeral_2EiDUB_2E1=1. c_2Elist_2EREVERSE_2E1=1. c_2Earithmetic_2EDIV2_2E1=1. c_2Earithmetic_2EEVEN_2E1=1. c_2Epred__set_2EREST_2E1=1. c_2Erelation_2Einv_2E1=1. c_2Epred__set_2EBIGINTER_2E1=1. c_2Erelation_2ERC_2E1=1. c_2Erelation_2Ereflexive_2E1=1. c_2Eset__relation_2Erange_2E1=1. c_2Ewhile_2ELEAST_2E1=1. c_2Enumpair_2Etri_2E1=1. c_2Eset__relation_2Edomain_2E1=1. c_2Ewhile_2EOLEAST_2E1=1. tyop_2Ebool_2Eitself=1. c_2Ebool_2E_7E_2E1=1. c_2Epred__set_2EMAX__SET_2E1=1. c_2Epred__set_2Ecount_2E1=1. c_2Epred__set_2ECHOICE_2E1=1. c_2Ecombin_2EK_2E1=1. c_2Edivides_2EPRIMES_2E1=1. c_2Epred__set_2ESING_2E1=1. c_2EfixedPoint_2Emonotone_2E1=1. c_2Elist_2EFLAT_2E1=1. c_2Elist_2ELAST_2E1=1. c_2Erelation_2ETC_2E1=1. c_2Edivides_2Eprime_2E1=1. c_2Eind__type_2EZRECSPACE_2E1=1. c_2Eoption_2EIS__SOME_2E1=1. c_2Epred__set_2EMIN__SET_2E1=1. c_2Erelation_2Esymmetric_2E1=1. c_2Elist_2ESUM_2E1=1. c_2Eset__relation_2Eacyclic_2E1=1. c_2Epred__set_2ECOMPL_2E1=1. c_2Elogroot_2ESQRTd_2E1=1. c_2Erelation_2Eantisymmetric_2E1=1. c_2Erelation_2EEQC_2E1=1. c_2Eset__relation_2Etransitive_2E1=1. c_2Eoption_2Esome_2E1=1. c_2Elist_2ENULL_2E1=1. c_2Elist_2Enub_2E1=1. c_2Emin_2E_3D_2E1=1. c_2Erelation_2ERDOM_2E1=1. c_2Erelation_2EWeakOrder_2E1=1. c_2Erelation_2Etotal_2E1=1. c_2Esum_2EIS__SUM__REP_2E1=1. c_2EfixedPoint_2Elfp_2E1=1. c_2Elist_2ETL_2E1=1. c_2Enumeral_2Eexactlog_2E1=1. c_2Enumeral_2EiiSUC_2E1=1. c_2Enumeral__bit_2EFDUB_2E1=1. c_2Eoption_2ETHE_2E1=1. c_2Egcdset_2Egcdset_2E1=1. c_2Elist_2EFRONT_2E1=1. c_2Epred__set_2ESUM__SET_2E1=1. c_2Erelation_2ERTC_2E1=1. c_2Erelation_2ESC_2E1=1. c_2Earithmetic_2EDIVMOD_2E1=1. c_2Ebit_2ELOG2_2E1=1. c_2Ebool_2EDATATYPE_2E1=1. c_2Ebool_2EONE__ONE_2E1=1. c_2Eposet_2Ecomplete_2E1=1. c_2Epred__set_2EPOW_2E1=1. c_2Erelation_2Etrichotomous_2E1=1. c_2Eset__relation_2Eantisym_2E1=1. c_2Earithmetic_2EFACT_2E1=1. c_2Earithmetic_2Efindq_2E1=1. c_2Elist_2ESET__TO__LIST_2E1=1. c_2Enumeral_2EiZ_2E1=1. c_2Ecombin_2EASSOC_2E1=1. c_2Ecombin_2EI_2E1=1. c_2Elist_2EHD_2E1=1. c_2Elist_2EUNZIP_2E1=1. c_2Erelation_2EINVOL_2E1=1. c_2Erelation_2Ediamond_2E1=1. c_2Erelation_2Eirreflexive_2E1=1. c_2Enumeral__bit_2EiDIV2_2E1=1. c_2Enumpair_2Ensnd_2E1=1. c_2Erelation_2EStrongOrder_2E1=1. c_2Enumpair_2Einvtri_2E1=1. c_2Epair_2EABS__prod_2E1=1. c_2Erelation_2EIDEM_2E1=1. c_2Erelation_2EOrder_2E1=1. c_2Erelation_2Eequivalence_2E1=1. c_2Eset__relation_2Estrict_2E1=1. c_2Earithmetic_2E_2B_2E1=1. c_2EfixedPoint_2Egfp_2E1=1. c_2Enumeral__bit_2EiSUC_2E1=1. c_2Eoption_2EIS__NONE_2E1=1. c_2Eposet_2Ecarrier_2E1=1. c_2Esum_2EABS__sum_2E1=1. c_2Eind__type_2Edest__rec_2E1=1. c_2Elist_2EMAP_2E1=1. c_2Enumeral__bit_2EiLOG2_2E1=1. c_2Enumpair_2Enfst_2E1=1. c_2Eprim__rec_2Emeasure_2E1=1. c_2Ebit_2ELOWEST__SET__BIT_2E1=1. c_2Eind__type_2Emk__rec_2E1=1. c_2Enum_2EIS__NUM__REP_2E1=1. c_2Epair_2EREP__prod_2E1=1. c_2Epred__set_2EIMAGE_2E1=1. c_2Erelation_2EWeakLinearOrder_2E1=1. c_2Erelation_2Ercdiamond_2E1=1. c_2Ebool_2EONTO_2E1=1. c_2Eind__type_2EINJN_2E1=1. c_2Eoption_2EOPTION__GUARD_2E1=1. c_2Eoption_2EOPTION__JOIN_2E1=1. c_2Eoption_2EOPTION__MAP_2E1=1. c_2Epair_2ECURRY_2E1=1. c_2Epred__set_2EPROD__SET_2E1=1. c_2Erelation_2EWCR_2E1=1. c_2Esum_2EISL_2E1=1. c_2Eind__type_2EINJA_2E1=1. c_2Eind__type_2EINJF_2E1=1. c_2Enum_2EABS__num_2E1=1. c_2Eoption_2Eoption__ABS_2E1=1. c_2Epred__set_2Eenumerate_2E1=1. c_2Erelation_2ESTRORD_2E1=1. c_2Esum_2EISR_2E1=1. c_2Ecombin_2ECOMM_2E1=1. c_2Elist_2EoHD_2E1=1. c_2Elogroot_2EiSQRT0_2E1=1. c_2Elogroot_2EiSQRT1_2E1=1. c_2Elogroot_2EiSQRT2_2E1=1. c_2Elogroot_2EiSQRT3_2E1=1. c_2Enum_2EREP__num_2E1=1. c_2Enumeral_2EiSQR_2E1=1. c_2Epred__set_2Epair__to__num_2E1=1. c_2Erelation_2ECR_2E1=1. c_2Ecombin_2EC_2E1=1. c_2Ecombin_2Eo_2E1=1. c_2Eind__type_2ENUMRIGHT_2E1=1. c_2Elist_2ESHORTLEX_2E1=1. c_2EnormalForms_2EUNIV__POINT_2E1=1. c_2Enum_2ESUC__REP_2E1=1. c_2Enumpair_2Enlen_2E1=1. c_2Eoption_2Eoption__REP_2E1=1. c_2Epred__set_2EINSERT_2E1=1. c_2Epred__set_2EPREIMAGE_2E1=1. c_2Epred__set_2Enum__to__pair_2E1=1. c_2Erelation_2ELinearOrder_2E1=1. c_2Erelation_2EPreOrder_2E1=1. c_2Erelation_2EStrongLinearOrder_2E1=1. c_2Eset__relation_2Euniv__reln_2E1=1. c_2Esum_2EOUTL_2E1=1. c_2Esum_2EOUTR_2E1=1. c_2Esum_2EREP__sum_2E1=1. c_2Ebool_2EBOUNDED_2E1=1. c_2Eind__type_2ENUMFST_2E1=1. c_2Eind__type_2ENUMLEFT_2E1=1. c_2Eind__type_2ENUMSND_2E1=1. c_2Elist_2ELLEX_2E1=1. c_2Emarker_2Estmarker_2E1=1. c_2Epred__set_2EEMPTY_2E1=1. c_2Epred__set_2EUNIV_2E1=1. c_2Eprim__rec_2Ewellfounded_2E1=1. c_2Erelation_2ERRANGE_2E1=1. c_2Erelation_2ESN_2E1=1. c_2Erelation_2Ediag_2E1=1. c_2Eset__relation_2Erel__to__reln_2E1=1. c_2Earithmetic_2Enat__elim____magic_2E1=1. c_2EbasicSize_2Ebool__size_2E1=1. c_2EbasicSize_2Eone__size_2E1=1. c_2Ebit_2EBIT_2E1=1. c_2EfixedPoint_2Eempty_2E1=1. c_2Eind__type_2EFNIL_2E1=1. c_2Elist_2EEL_2E1=1. c_2Elist_2EFIND_2E1=1. c_2Elist_2EINDEX__OF_2E1=1. c_2Elist_2ELIST__GUARD_2E1=1. c_2Elist_2EdropWhile_2E1=1. c_2Elogroot_2ELOG_2E1=1. c_2Emarker_2EAbbrev_2E1=1. c_2Emarker_2ECong_2E1=1. c_2Emarker_2Eunint_2E1=1. c_2Enumpair_2Enmap_2E1=1. c_2Epair_2ESWAP_2E1=1. c_2Eposet_2Erelation_2E1=1. c_2Epred__set_2EPROD__IMAGE_2E1=1. c_2Epred__set_2ESUM__IMAGE_2E1=1. c_2Erelation_2ERCOMPL_2E1=1. c_2Erelation_2Einv__image_2E1=1. c_2Eset__relation_2Ereln__to__rel_2E1=1. f11=1. f20=1. f274=1. f277=1. f278=1. f279=1. f282=1. f283=1. f732=1. f733=1. f736=1. f737=1. f762=1. f771=1. f772=1. f775=1. f776=1. f778=1. f789=1. f791=1. f792=1. f811=1. f812=1. f818=1. f819=1. f820=1. f828=1. f834=1. f839=1. f840=1. f844=1. f847=1. f864=1. f866=1. f867=1. f872=1. f873=1. f874=1. f953=1. f954=1. f955=1. f956=1. f960=1. f961=1. f975=1. f976=1. f982=1. f999=1. f1032=1. f1036=1. f1037=1. f1038=1. f1039=1. f1040=1. f1041=1. f1043=1. f1044=1. f1064=1. f1101=1. f1102=1. f1103=1. f1104=1. f1105=1. f1106=1. f1107=1. f1108=1. f1109=1. f1110=1. f1112=1. f1113=1. f1116=1. f1144=1. f1145=1. f1146=1. f1156=1. f1157=1. f1158=1. f1159=1. f1161=1. f1162=1. f1163=1. f1164=1. f1165=1. f1166=1. f1167=1. f1168=1. f1170=1. f1171=1. f1178=1. f1179=1. f1180=1. f1181=1. f1183=1. f1184=1. f1194=1. f1196=1. f1197=1. f1198=1. f1199=1. f1201=1. f1202=1. f1215=1. f1216=1. f1278=1. f1279=1. f1356=1. f1399=1. f1400=1. f1416=1. f1487=1. f1488=1. f1781=1. f2006=1. f2007=1. f2008=1. c_2Ebool_2ECOND_2E3=1. c_2Elist_2ELIST__REL_2E3=1. c_2Erelation_2ETC_2E3=1. c_2Erelation_2ERTC_2E3=1. c_2Epred__set_2EBIJ_2E3=1. c_2Epred__set_2EINJ_2E3=1. c_2Ebit_2EBITS_2E3=1. c_2Erelation_2EEQC_2E3=1. c_2Elist_2ELUPDATE_2E3=1. c_2Ecombin_2EUPDATE_2E3=1. c_2Enumeral_2EiSUB_2E3=1. c_2Earithmetic_2EFUNPOW_2E3=1. c_2Epred__set_2ESURJ_2E3=1. c_2Ewhile_2EHOARE__SPEC_2E3=1. c_2Eposet_2Eglb_2E3=1. c_2Eposet_2Elub_2E3=1. c_2Elist_2ESHORTLEX_2E3=1. c_2Earithmetic_2EMODEQ_2E3=1. c_2Elist_2ELLEX_2E3=1. c_2Eoption_2Eoption__CASE_2E3=1. c_2Ebit_2ESLICE_2E3=1. c_2Elist_2Elist__CASE_2E3=1. c_2Enumeral__bit_2ESFUNPOW_2E3=1. c_2Elist_2EFOLDL_2E3=1. c_2Erelation_2ERC_2E3=1. c_2Eoption_2EOPTION__MAP2_2E3=1. c_2Epair_2EPROD__ALL_2E3=1. c_2Elist_2EMAP2_2E3=1. c_2Epred__set_2EITSET_2E3=1. c_2Egcd_2Eis__gcd_2E3=1. c_2Earithmetic_2Enum__CASE_2E3=1. c_2Esum_2ESUM__ALL_2E3=1. c_2Ewhile_2EOWHILE_2E3=1. c_2Eind__type_2ECONSTR_2E3=1. c_2Enumeral__bit_2EBIT__REV_2E3=1. c_2Eoption_2EOPTREL_2E3=1. c_2Erelation_2ESC_2E3=1. c_2Elist_2EsplitAtPki_2E3=1. c_2Esum_2Esum__CASE_2E3=1. c_2Elist_2EFOLDR_2E3=1. c_2Enumpair_2Enlistrec_2E3=1. c_2Epred__set_2ELINV__OPT_2E3=1. c_2Ebit_2EMOD__2EXP__EQ_2E3=1. c_2Ebit_2ESIGN__EXTEND_2E3=1. c_2Ecombin_2Eo_2E3=1. c_2Elist_2EGENLIST__AUX_2E3=1. c_2Eposet_2Egfp_2E3=1. c_2Eposet_2Elfp_2E3=1. c_2Erelation_2ERESTRICT_2E3=1. c_2Eind__type_2EZCONSTR_2E3=1. c_2Epred__set_2Eis__measure__maximal_2E3=1. c_2Ebit_2EBIT__MODIFY_2E3=1. c_2Eposet_2Efunction_2E3=1. c_2Epred__set_2EDFUNSET_2E3=1. c_2Epred__set_2EFUNSET_2E3=1. c_2Erelation_2EINDUCTIVE__INVARIANT_2E3=1. c_2Ecombin_2ES_2E3=1. c_2Epair_2E_23_23_2E3=1. c_2Epred__set_2EINSERT_2E3=1. c_2Ewhile_2EWHILE_2E3=1. c_2Ecombin_2EC_2E3=1. c_2EfixedPoint_2Efnsum_2E3=1. c_2Eind__type_2EFCONS_2E3=1. c_2Enumpair_2Enfoldl_2E3=1. c_2Eprim__rec_2EPRIM__REC_2E3=1. c_2Eprim__rec_2ESIMP__REC_2E3=1. c_2Erelation_2EWFREC_2E3=1. c_2Esum_2E_2B_2B_2E3=1. c_2Ebool_2ERES__ABSTRACT_2E3=1. c_2Elist_2EINDEX__FIND_2E3=1. c_2Epred__set_2ECROSS_2E3=1. c_2Epred__set_2EIMAGE_2E3=1. c_2Epred__set_2EINTER_2E3=1. c_2Epred__set_2ELINV_2E3=1. c_2Epred__set_2EUNION_2E3=1. c_2Erelation_2Ediag_2E3=1. c_2Eset__relation_2ERRUNIV_2E3=1. c_2EbasicSize_2Esum__size_2E3=1. c_2Eind__type_2EINJA_2E3=1. c_2Eind__type_2EINJN_2E3=1. c_2Epred__set_2EDELETE_2E3=1. c_2Epred__set_2EDIFF_2E3=1. c_2Epred__set_2ERINV_2E3=1. c_2Epred__set_2Eschroeder__close_2E3=1. c_2Erelation_2ESTRORD_2E3=1. c_2Erelation_2Ethe__fun_2E3=1. c_2Eset__relation_2Ereln__to__rel_2E3=1. c_2Elist_2ELIST__LIFT2_2E3=1. c_2Elist_2EPAD__LEFT_2E3=1. c_2Elist_2EPAD__RIGHT_2E3=1. c_2Eoption_2EOPTION__MCOMP_2E3=1. c_2Epair_2ECURRY_2E3=1. c_2Epred__set_2EPREIMAGE_2E3=1. c_2Eprim__rec_2Emeasure_2E3=1. c_2Erelation_2ERCOMPL_2E3=1. c_2Erelation_2Einv_2E3=1. f4=1. f6=1. f7=1. f12=1. f13=1. f15=1. f16=1. f17=1. f24=1. f25=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f45=1. f46=1. f53=1. f54=1. f56=1. f57=1. f58=1. f67=1. f68=1. f69=1. f72=1. f73=1. f79=1. f80=1. f81=1. f82=1. f83=1. f89=1. f97=1. f98=1. f99=1. f109=1. f113=1. f114=1. f115=1. f122=1. f123=1. f125=1. f126=1. f127=1. f128=1. f129=1. f130=1. f131=1. f132=1. f133=1. f135=1. f136=1. f138=1. f139=1. f148=1. f149=1. f155=1. f156=1. f161=1. f162=1. f163=1. f170=1. f171=1. f176=1. f177=1. f178=1. f181=1. f182=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1. f203=1. f204=1. f213=1. f224=1. f225=1. f226=1. f228=1. f229=1. f230=1. f243=1. f244=1. f265=1. f266=1. f267=1. f268=1. f292=1. f296=1. f297=1. f298=1. f299=1. f300=1. f301=1. f302=1. f303=1. f304=1. f305=1. f306=1. f307=1. f308=1. f309=1. f310=1. f311=1. f312=1. f313=1. f317=1. f318=1. f319=1. f320=1. f321=1. f322=1. f336=1. f337=1. f338=1. f339=1. f340=1. f342=1. f343=1. f344=1. f345=1. f347=1. f348=1. f349=1. f350=1. f351=1. f352=1. f353=1. f354=1. f358=1. f359=1. f360=1. f361=1. f362=1. f363=1. f364=1. f365=1. f366=1. f367=1. f370=1. f371=1. f372=1. f373=1. f378=1. f379=1. f380=1. f381=1. f382=1. f383=1. f384=1. f392=1. f405=1. f406=1. f407=1. f408=1. f409=1. f410=1. f411=1. f412=1. f413=1. f414=1. f415=1. f416=1. f428=1. f429=1. f430=1. f431=1. f432=1. f433=1. f436=1. f437=1. f438=1. f439=1. f440=1. f446=1. f447=1. f448=1. f449=1. f451=1. f452=1. f453=1. f462=1. f463=1. f469=1. f471=1. f474=1. f475=1. f476=1. f477=1. f490=1. f492=1. f496=1. f508=1. f509=1. f512=1. f513=1. f515=1. f516=1. f517=1. f520=1. f521=1. f522=1. f530=1. f531=1. f532=1. f533=1. f534=1. f535=1. f539=1. f540=1. f541=1. f542=1. f556=1. f563=1. f569=1. f570=1. f571=1. f572=1. f580=1. f581=1. f582=1. f583=1. f593=1. f594=1. f597=1. f598=1. f599=1. f600=1. f601=1. f602=1. f603=1. f607=1. f608=1. f609=1. f616=1. f617=1. f618=1. f619=1. f621=1. f622=1. f623=1. f637=1. f638=1. f640=1. f641=1. f642=1. f645=1. f646=1. f647=1. f648=1. f649=1. f650=1. f680=1. f681=1. f686=1. f687=1. f690=1. f691=1. f692=1. f713=1. f714=1. f715=1. f724=1. f725=1. f726=1. f727=1. f728=1. f729=1. f731=1. f752=1. f753=1. f754=1. f755=1. f756=1. f757=1. f759=1. f765=1. f766=1. f767=1. f773=1. f774=1. f786=1. f787=1. f825=1. f830=1. f835=1. f836=1. f837=1. f838=1. f842=1. f843=1. f865=1. f887=1. f888=1. f889=1. f890=1. f891=1. f892=1. f894=1. f899=1. f900=1. f901=1. f902=1. f912=1. f913=1. f930=1. f931=1. f932=1. f933=1. f934=1. f935=1. f936=1. f937=1. f986=1. f987=1. f988=1. f989=1. f990=1. f991=1. f1000=1. f1001=1. f1002=1. f1003=1. f1004=1. f1005=1. f1006=1. f1007=1. f1008=1. f1025=1. f1026=1. f1027=1. f1028=1. f1060=1. f1061=1. f1062=1. f1068=1. f1069=1. f1070=1. f1071=1. f1118=1. f1131=1. f1132=1. f1133=1. f1134=1. f1147=1. f1148=1. f1149=1. f1150=1. f1172=1. f1173=1. f1174=1. f1175=1. f1176=1. f1177=1. f1205=1. f1219=1. f1221=1. f1227=1. f1236=1. f1242=1. f1243=1. f1244=1. f1249=1. f1270=1. f1271=1. f1272=1. f1273=1. f1275=1. f1281=1. f1282=1. f1283=1. f1284=1. f1285=1. f1286=1. f1287=1. f1288=1. f1300=1. f1301=1. f1302=1. f1303=1. f1304=1. f1308=1. f1309=1. f1310=1. f1311=1. f1312=1. f1313=1. f1314=1. f1323=1. f1324=1. f1325=1. f1326=1. f1327=1. f1328=1. f1329=1. f1331=1. f1332=1. f1352=1. f1353=1. f1354=1. f1372=1. f1373=1. f1374=1. f1375=1. f1376=1. f1377=1. f1381=1. f1387=1. f1388=1. f1389=1. f1393=1. f1395=1. f1396=1. f1397=1. f1401=1. f1402=1. f1403=1. f1404=1. f1406=1. f1407=1. f1408=1. f1409=1. f1410=1. f1411=1. f1414=1. f1415=1. f1420=1. f1421=1. f1422=1. f1423=1. f1424=1. f1425=1. f1426=1. f1427=1. f1428=1. f1432=1. f1450=1. f1451=1. f1452=1. f1453=1. f1454=1. f1460=1. f1461=1. f1470=1. f1476=1. f1477=1. f1478=1. f1479=1. f1480=1. f1481=1. f1482=1. f1483=1. f1484=1. f1485=1. f1486=1. f1491=1. f1495=1. f1496=1. f1498=1. f1500=1. f1502=1. f1503=1. f1504=1. f1505=1. f1510=1. f1511=1. f1512=1. f1513=1. f1515=1. f1516=1. f1517=1. f1532=1. f1536=1. f1537=1. f1538=1. f1539=1. f1540=1. f1541=1. f1542=1. f1543=1. f1547=1. f1558=1. f1560=1. f1561=1. f1562=1. f1563=1. f1568=1. f1569=1. f1570=1. f1571=1. f1574=1. f1580=1. f1581=1. f1582=1. f1586=1. f1587=1. f1604=1. f1614=1. f1635=1. f1636=1. f1648=1. f1649=1. f1650=1. f1651=1. f1652=1. f1653=1. f1654=1. f1656=1. f1662=1. f1670=1. f1671=1. f1672=1. f1673=1. f1674=1. f1680=1. f1681=1. f1682=1. f1683=1. f1693=1. f1694=1. f1704=1. f1705=1. f1706=1. f1713=1. f1714=1. f1715=1. f1716=1. f1717=1. f1718=1. f1719=1. f1726=1. f1727=1. f1728=1. f1734=1. f1739=1. f1740=1. f1742=1. f1743=1. f1744=1. f1745=1. f1752=1. f1756=1. f1757=1. f1758=1. f1759=1. f1771=1. f1772=1. f1775=1. f1776=1. f1789=1. f1790=1. f1796=1. f1797=1. f1829=1. f1830=1. f1850=1. f1851=1. f1852=1. f1853=1. f1858=1. f1864=1. f1866=1. f1867=1. f1868=1. f1869=1. f1880=1. f1908=1. f1909=1. f1910=1. f1916=1. f1934=1. f1935=1. f1936=1. f1937=1. f1938=1. f1939=1. f1940=1. f1959=1. f1960=1. f1961=1. f1994=1. f1995=1. f1996=1. f1997=1. f1998=1. f1999=1. f2000=1. f2001=1. f2018=1. f2019=1. f2020=1. f2021=1. f2090=1. f2091=1. f2092=1. f2093=1. f2094=1. f2095=1. f2096=1. f2104=1. f2105=1. f2106=1. f2107=1. f2109=1. f2110=1. f2111=1. f2112=1. f2113=1. f2128=1. f2129=1. f2130=1. f2131=1. f2153=1. f2161=1. f2162=1. f2163=1. f2164=1. f2179=1. f2188=1. f2189=1. f2190=1. f2191=1. f2197=1. f2198=1. f2199=1. f2200=1. f2201=1. f2202=1. f2203=1. f2204=1. f2205=1. f2206=1. f2207=1. f2208=1. f2209=1. f2210=1. f2211=1. f2212=1. f2213=1. f2214=1. f2215=1. f2216=1. f2217=1. f2218=1. f2219=1. f2220=1. f2221=1. f2222=1. f2223=1. f2224=1. f2225=1. f2226=1. f2227=1. f2228=1. f2229=1. f2230=1. f2231=1. f2232=1. f2233=1. f2257=1. f2258=1. f2259=1. f2260=1. f2261=1. f2262=1. f2263=1. f2265=1. f2266=1. f2267=1. f2268=1. f2269=1. f2270=1. f2281=1. f2282=1. f2283=1. f2284=1. f2285=1. f2286=1. f2287=1. f2288=1. f2289=1. f2290=1. f2291=1. f2292=1. f2293=1. f2294=1. f2295=1. f2296=1. f2297=1. f2305=1. f2306=1. c_2Earithmetic_2ENRC_2E4=1. c_2Epair_2ELEX_2E4=1. c_2Ebit_2EBITWISE_2E4=1. c_2Elist_2ELRC_2E4=1. c_2Elist_2EFOLDL2_2E4=1. c_2Eprim__rec_2ESIMP__REC__REL_2E4=1. c_2Enumeral__bit_2EiBITWISE_2E4=1. c_2Enumeral_2EiBIT__cases_2E4=1. c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4=1. c_2Ecombin_2EUPDATE_2E4=1. c_2Epred__set_2EREL__RESTRICT_2E4=1. c_2Eprim__rec_2EPRIM__REC__FUN_2E4=1. c_2Erelation_2EO_2E4=1. c_2Erelation_2ERINTER_2E4=1. c_2Erelation_2ERRESTRICT_2E4=1. c_2Erelation_2ERUNION_2E4=1. c_2Erelation_2Eapprox_2E4=1. c_2Erelation_2ERDOM__DELETE_2E4=1. c_2Erelation_2ERESTRICT_2E4=1. c_2Erelation_2Einv__image_2E4=1. c_2Eind__type_2EINJP_2E4=1. f2=1. f5=1. f14=1. f26=1. f27=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f134=1. f140=1. f141=1. f142=1. f143=1. f165=1. f166=1. f167=1. f168=1. f169=1. f172=1. f179=1. f205=1. f206=1. f207=1. f208=1. f218=1. f219=1. f220=1. f221=1. f227=1. f234=1. f238=1. f239=1. f242=1. f245=1. f246=1. f247=1. f248=1. f249=1. f261=1. f262=1. f263=1. f264=1. f269=1. f270=1. f271=1. f273=1. f285=1. f291=1. f293=1. f314=1. f330=1. f333=1. f355=1. f356=1. f357=1. f376=1. f377=1. f385=1. f386=1. f387=1. f388=1. f389=1. f390=1. f391=1. f393=1. f396=1. f397=1. f398=1. f399=1. f404=1. f417=1. f420=1. f422=1. f434=1. f444=1. f445=1. f454=1. f461=1. f464=1. f480=1. f481=1. f482=1. f485=1. f486=1. f487=1. f497=1. f498=1. f499=1. f514=1. f545=1. f546=1. f547=1. f573=1. f576=1. f584=1. f585=1. f590=1. f610=1. f611=1. f612=1. f613=1. f614=1. f615=1. f620=1. f624=1. f636=1. f639=1. f658=1. f659=1. f660=1. f661=1. f662=1. f663=1. f664=1. f665=1. f666=1. f667=1. f670=1. f671=1. f672=1. f673=1. f674=1. f675=1. f676=1. f677=1. f678=1. f679=1. f707=1. f716=1. f717=1. f734=1. f735=1. f742=1. f743=1. f761=1. f810=1. f826=1. f831=1. f833=1. f876=1. f877=1. f881=1. f882=1. f886=1. f893=1. f928=1. f939=1. f952=1. f962=1. f963=1. f964=1. f965=1. f966=1. f967=1. f968=1. f969=1. f970=1. f971=1. f972=1. f973=1. f974=1. f983=1. f984=1. f985=1. f993=1. f995=1. f1013=1. f1017=1. f1018=1. f1019=1. f1020=1. f1021=1. f1022=1. f1024=1. f1030=1. f1063=1. f1075=1. f1076=1. f1077=1. f1078=1. f1079=1. f1080=1. f1082=1. f1095=1. f1096=1. f1097=1. f1117=1. f1151=1. f1152=1. f1192=1. f1214=1. f1223=1. f1228=1. f1229=1. f1239=1. f1240=1. f1246=1. f1252=1. f1253=1. f1254=1. f1255=1. f1256=1. f1257=1. f1258=1. f1259=1. f1263=1. f1264=1. f1265=1. f1266=1. f1267=1. f1268=1. f1269=1. f1293=1. f1297=1. f1305=1. f1315=1. f1334=1. f1357=1. f1359=1. f1360=1. f1362=1. f1363=1. f1364=1. f1371=1. f1378=1. f1380=1. f1386=1. f1417=1. f1418=1. f1433=1. f1434=1. f1435=1. f1445=1. f1446=1. f1447=1. f1459=1. f1462=1. f1463=1. f1464=1. f1465=1. f1466=1. f1467=1. f1497=1. f1514=1. f1518=1. f1523=1. f1524=1. f1525=1. f1526=1. f1527=1. f1528=1. f1529=1. f1530=1. f1548=1. f1550=1. f1551=1. f1552=1. f1553=1. f1554=1. f1566=1. f1567=1. f1572=1. f1573=1. f1575=1. f1585=1. f1593=1. f1595=1. f1596=1. f1597=1. f1598=1. f1599=1. f1600=1. f1601=1. f1602=1. f1641=1. f1642=1. f1643=1. f1644=1. f1657=1. f1658=1. f1659=1. f1660=1. f1661=1. f1669=1. f1675=1. f1676=1. f1686=1. f1687=1. f1688=1. f1689=1. f1690=1. f1691=1. f1695=1. f1709=1. f1741=1. f1748=1. f1753=1. f1761=1. f1762=1. f1763=1. f1764=1. f1765=1. f1766=1. f1767=1. f1768=1. f1769=1. f1770=1. f1791=1. f1792=1. f1808=1. f1809=1. f1810=1. f1811=1. f1819=1. f1820=1. f1821=1. f1822=1. f1823=1. f1836=1. f1837=1. f1841=1. f1854=1. f1855=1. f1856=1. f1857=1. f1881=1. f1885=1. f1886=1. f1887=1. f1888=1. f1889=1. f1890=1. f1891=1. f1892=1. f1893=1. f1894=1. f1895=1. f1896=1. f1897=1. f1898=1. f1899=1. f1900=1. f1901=1. f1902=1. f1903=1. f1904=1. f1905=1. f1906=1. f1907=1. f1922=1. f1923=1. f1941=1. f1942=1. f1946=1. f1951=1. f1952=1. f1953=1. f1957=1. f1958=1. f1967=1. f1979=1. f1985=1. f1992=1. f1993=1. f2002=1. f2003=1. f2004=1. f2023=1. f2024=1. f2025=1. f2026=1. f2027=1. f2028=1. f2031=1. f2032=1. f2046=1. f2049=1. f2050=1. f2067=1. f2068=1. f2069=1. f2070=1. f2071=1. f2072=1. f2073=1. f2074=1. f2075=1. f2097=1. f2098=1. f2099=1. f2100=1. f2101=1. f2102=1. f2114=1. f2116=1. f2117=1. f2118=1. f2119=1. f2120=1. f2121=1. f2122=1. f2123=1. f2124=1. f2125=1. f2126=1. f2127=1. f2132=1. f2133=1. f2134=1. f2135=1. f2136=1. f2140=1. f2154=1. f2155=1. f2156=1. f2157=1. f2158=1. f2159=1. f2160=1. f2170=1. f2171=1. f2172=1. f2173=1. f2174=1. f2175=1. f2181=1. f2182=1. f2195=1. f2196=1. f2246=1. f2247=1. f2248=1. f2249=1. f2250=1. f2251=1. f2252=1. f2253=1. f2254=1. f2255=1. f2256=1. f2279=1. f2280=1. f2298=1. f2299=1. f2300=1. f2301=1. f2302=1. f2303=1. f2304=1. f70=1. f144=1. f150=1. f151=1. f152=1. f153=1. f154=1. f180=1. f183=1. f184=1. f185=1. f186=1. f187=1. f196=1. f197=1. f198=1. f199=1. f200=1. f212=1. f217=1. f251=1. f252=1. f253=1. f289=1. f290=1. f323=1. f324=1. f325=1. f326=1. f327=1. f328=1. f329=1. f334=1. f335=1. f368=1. f369=1. f400=1. f401=1. f402=1. f403=1. f418=1. f419=1. f426=1. f427=1. f455=1. f456=1. f460=1. f483=1. f484=1. f488=1. f489=1. f494=1. f495=1. f503=1. f504=1. f510=1. f524=1. f525=1. f526=1. f527=1. f528=1. f529=1. f554=1. f555=1. f557=1. f566=1. f567=1. f579=1. f587=1. f643=1. f644=1. f688=1. f689=1. f758=1. f763=1. f848=1. f849=1. f850=1. f851=1. f852=1. f853=1. f854=1. f855=1. f856=1. f857=1. f858=1. f859=1. f860=1. f861=1. f862=1. f879=1. f880=1. f895=1. f910=1. f911=1. f916=1. f917=1. f919=1. f920=1. f926=1. f927=1. f997=1. f998=1. f1014=1. f1046=1. f1047=1. f1048=1. f1049=1. f1086=1. f1120=1. f1121=1. f1122=1. f1123=1. f1124=1. f1125=1. f1126=1. f1127=1. f1128=1. f1135=1. f1136=1. f1137=1. f1138=1. f1139=1. f1140=1. f1141=1. f1142=1. f1143=1. f1232=1. f1245=1. f1260=1. f1261=1. f1262=1. f1316=1. f1317=1. f1318=1. f1319=1. f1320=1. f1335=1. f1336=1. f1337=1. f1338=1. f1339=1. f1340=1. f1341=1. f1342=1. f1343=1. f1344=1. f1345=1. f1346=1. f1347=1. f1348=1. f1349=1. f1361=1. f1365=1. f1369=1. f1370=1. f1379=1. f1383=1. f1384=1. f1392=1. f1405=1. f1412=1. f1439=1. f1440=1. f1468=1. f1469=1. f1492=1. f1493=1. f1494=1. f1509=1. f1519=1. f1520=1. f1522=1. f1555=1. f1556=1. f1557=1. f1564=1. f1578=1. f1579=1. f1605=1. f1640=1. f1655=1. f1664=1. f1696=1. f1697=1. f1698=1. f1699=1. f1731=1. f1735=1. f1736=1. f1746=1. f1747=1. f1749=1. f1773=1. f1774=1. f1782=1. f1783=1. f1784=1. f1785=1. f1786=1. f1787=1. f1788=1. f1798=1. f1799=1. f1800=1. f1801=1. f1802=1. f1803=1. f1804=1. f1805=1. f1806=1. f1807=1. f1812=1. f1813=1. f1814=1. f1871=1. f1882=1. f1911=1. f1921=1. f1930=1. f1931=1. f1943=1. f1944=1. f1947=1. f1954=1. f1955=1. f1956=1. f1980=1. f1986=1. f1987=1. f1988=1. f1989=1. f1990=1. f1991=1. f2022=1. f2053=1. f2054=1. f2055=1. f2056=1. f2057=1. f2058=1. f2059=1. f2060=1. f2061=1. f2062=1. f2065=1. f2078=1. f2079=1. f2080=1. f2081=1. f2082=1. f2083=1. f2084=1. f2085=1. f2086=1. f2087=1. f2088=1. f2089=1. f2108=1. f2237=1. f2238=1. f2239=1. f2240=1. f2241=1. f2242=1. f2243=1. f2244=1. f2245=1. f2271=1. f2272=1. f2273=1. f2274=1. f2275=1. f2276=1. f2277=1. f2278=1. c_2Enumeral__bit_2EBIT__MODF_2E6=1. f90=1. f124=1. f424=1. f425=1. f549=1. f552=1. f553=1. f568=1. f586=1. f604=1. f605=1. f625=1. f626=1. f627=1. f628=1. f629=1. f630=1. f631=1. f651=1. f652=1. f653=1. f654=1. f655=1. f656=1. f657=1. f693=1. f694=1. f695=1. f696=1. f697=1. f698=1. f764=1. f808=1. f878=1. f918=1. f940=1. f941=1. f942=1. f943=1. f944=1. f945=1. f946=1. f947=1. f948=1. f949=1. f950=1. f951=1. f1073=1. f1087=1. f1088=1. f1089=1. f1090=1. f1091=1. f1092=1. f1093=1. f1094=1. f1274=1. f1298=1. f1366=1. f1367=1. f1368=1. f1413=1. f1429=1. f1441=1. f1442=1. f1443=1. f1499=1. f1577=1. f1606=1. f1607=1. f1608=1. f1609=1. f1615=1. f1616=1. f1617=1. f1618=1. f1619=1. f1620=1. f1621=1. f1622=1. f1623=1. f1624=1. f1625=1. f1626=1. f1663=1. f1684=1. f1685=1. f1720=1. f1721=1. f1737=1. f1738=1. f1779=1. f1780=1. f1831=1. f1832=1. f1859=1. f1860=1. f1865=1. f1872=1. f1873=1. f1932=1. f1933=1. f1966=1. f1975=1. f1976=1. f1984=1. f2034=1. f2035=1. f2036=1. f2037=1. f2038=1. f2039=1. f2040=1. f2041=1. f2042=1. f2043=1. f2044=1. f2045=1. f2141=1. f2142=1. f2143=1. f2144=1. f2145=1. f2146=1. f2147=1. f2148=1. f2149=1. f2150=1. f2151=1. f2152=1. f2192=1. f2193=1. f288=1. f467=1. f537=1. f538=1. f564=1. f565=1. f668=1. f669=1. f708=1. f709=1. f710=1. f711=1. f779=1. f793=1. f794=1. f795=1. f796=1. f797=1. f798=1. f799=1. f800=1. f801=1. f802=1. f803=1. f804=1. f805=1. f806=1. f807=1. f992=1. f1777=1. f1778=1. f1833=1. f1834=1. f1962=1. f1963=1. f2103=1. f2115=1. f423=1. f518=1. f519=1. f578=1. f632=1. f633=1. f634=1. f635=1. f682=1. f683=1. f684=1. f685=1. f1610=1. f1611=1. f1612=1. f1613=1. f1750=1. f1751=1. f1924=1. f1925=1. f543=1. f544=1. f559=1. f560=1. f1817=1. f1818=1. f699=1. f700=1. f701=1. f702=1. f703=1. f704=1. f705=1. f706=1. f1645=1. f1646=1. f1647=1. f1722=1. f1723=1. f1724=1. f1725=1. 17.24/17.19 17.24/17.19 ============================== STATISTICS ============================ 17.24/17.19 17.24/17.19 Given=0. Generated=6032. Kept=4209. proofs=0. 17.24/17.19 Usable=0. Sos=0. Demods=1040. Limbo=4208, Disabled=6032. Hints=0. 17.24/17.19 Kept_by_rule=0, Deleted_by_rule=0. 17.24/17.19 Forward_subsumed=1823. Back_subsumed=0. 17.24/17.19 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 17.24/17.19 New_demodulators=1040 (2 lex), Back_demodulated=0. Back_unit_deleted=0. 17.24/17.19 Demod_attempts=418321. Demod_rewrites=5826. 17.24/17.19 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 17.24/17.19 Nonunit_fsub_feature_tests=3232. Nonunit_bsub_feature_tests=0. 17.24/17.19 Megabytes=419.43. 17.24/17.19 User_CPU=10.92, System_CPU=0.12, Wall_clock=11. 17.24/17.19 17.24/17.19 Megs malloced by palloc(): 400. 17.24/17.19 type (bytes each) gets frees in use bytes 17.24/17.19 chunk ( 104) 415549 415549 0 0.0 K 17.24/17.19 string_buf ( 8) 346614 346614 0 0.0 K 17.24/17.19 token ( 20) 907640 907640 0 0.0 K 17.24/17.19 pterm ( 16) 610891 610891 0 0.0 K 17.24/17.19 hashtab ( 8) 5132 5132 0 0.0 K 17.24/17.19 hashnode ( 8) 17534 17534 0 0.0 K 17.24/17.19 term ( 20) 5977252 4946584 1030668 20130.2 K 17.24/17.19 term arg arrays: 4714.7 K 17.24/17.19 attribute ( 12) 38814 1588 37226 436.2 K 17.24/17.19 ilist ( 8) 106920884 106903554 17330 135.4 K 17.24/17.19 plist ( 8) 144198 82407 61791 482.7 K 17.24/17.19 i2list ( 12) 319683 319683 0 0.0 K 17.24/17.19 just ( 12) 26760 5688 21072 246.9 K 17.24/17.19 parajust ( 16) 0 0 0 0.0 K 17.24/17.19 instancejust ( 8) 0 0 0 0.0 K 17.24/17.19 ivyjust ( 24) 0 0 0 0.0 K 17.24/17.19 formula ( 28) 210395 139385 71010 1941.7 K 17.24/17.19 formula arg arrays: 237.3 K 17.24/17.19 topform ( 52) 20049 1823 18226 925.5 K 17.24/17.19 clist_pos ( 20) 20165 6032 14133 276.0 K 17.24/17.19 clist ( 16) 8 0 8 0.1 K 17.24/17.19 context ( 808) 71361 71361 0 0.0 K 17.24/17.19 trail ( 12) 15596 15596 0 0.0 K 17.24/17.19 ac_match_pos (70044) 0 0 0 0.0 K 17.24/17.19 ac_match_free_vars_pos (20020) 17.24/17.19 0 0 0 0.0 K 17.24/17.19 btm_state ( 60) 0 0 0 0.0 K 17.24/17.19 btu_state ( 60) 0 0 0 0.0 K 17.24/17.19 ac_position (285432) 0 0 0 0.0 K 17.24/17.19 fpa_trie ( 20) 86279 0 86279 1685.1 K 17.24/17.19 fpa_state ( 28) 3930 3930 0 0.0 K 17.24/17.19 fpa_index ( 12) 10 0 10 0.1 K 17.24/17.19 fpa_chunk ( 20) 43315 6872 36443 711.8 K 17.24/17.19 fpa_list ( 16) 29296 0 29296 457.8 K 17.24/17.19 fpa_list chunks: 754.2 K 17.24/17.19 discrim ( 12) 43811 0 43811 513.4 K 17.24/17.19 discrim_pos ( 16) 6053 6053 0 0.0 K 17.24/17.19 flat2 ( 32) 288814 288814 0 0.0 K 17.24/17.19 flat ( 48) 0 0 0 0.0 K 17.24/17.19 flatterm ( 32) 682160 682160 0 0.0 K 17.24/17.19 mindex ( 28) 13 0 13 0.4 K 17.24/17.19 mindex_pos ( 56) 51851 51851 0 0.0 K 17.24/17.19 lindex ( 12) 5 0 5 0.1 K 17.24/17.19 clash ( 40) 0 0 0 0.0 K 17.24/17.19 di_tree ( 12) 32031087 0 32031087 375364.3 K 17.24/17.19 avl_node ( 20) 0 0 0 0.0 K 17.24/17.19 17.24/17.19 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 17.24/17.19 List 1, length 21, 0.1 K 17.24/17.19 List 4, length 15, 0.2 K 17.24/17.19 List 5, length 9, 0.2 K 17.24/17.19 List 6, length 1, 0.0 K 17.24/17.19 List 7, length 25, 0.7 K 17.24/17.19 List 8, length 1763, 55.1 K 17.24/17.19 List 10, length 1, 0.0 K 17.24/17.19 List 12, length 2, 0.1 K 17.24/17.19 List 14, length 8, 0.4 K 17.24/17.19 List 15, length 8, 0.5 K 17.24/17.19 List 17, length 8, 0.5 K 17.24/17.19 List 18, length 2, 0.1 K 17.24/17.19 List 19, length 1, 0.1 K 17.24/17.19 List 20, length 2, 0.2 K 17.24/17.19 List 23, length 2, 0.2 K 17.24/17.19 List 26, length 894, 90.8 K 17.24/17.19 List 30, length 2, 0.2 K 17.24/17.19 List 32, length 27, 3.4 K 17.24/17.19 List 36, length 2, 0.3 K 17.24/17.19 List 39, length 2, 0.3 K 17.24/17.19 List 60, length 2, 0.5 K 17.24/17.19 List 202, length 2, 1.6 K 17.24/17.19 17.24/17.19 ============================== SELECTOR REPORT ======================= 17.24/17.19 Sos_deleted=0, Sos_displaced=0, Sos_size=0 17.24/17.19 SELECTOR PART PRIORITY ORDER SIZE SELECTED 17.24/17.19 I 2147483647 high age 0 0 17.24/17.19 H 1 high weight 0 0 17.24/17.19 A 1 low age 0 0 17.24/17.19 F 4 low weight 0 0 17.24/17.19 T 4 low weight 0 0 17.24/17.19 ============================== end of selector report ================ 17.24/17.19 17.24/17.19 ============================== end of statistics ===================== 17.24/17.19 17.24/17.19 Exiting with failure. 17.24/17.19 17.24/17.19 Process 31359 exit (max_megs) Tue Jul 13 15:18:53 2021 17.24/17.19 Prover9 interrupted 17.24/17.20 EOF