0.04/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.09 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.29 % Computer : n021.cluster.edu 0.09/0.29 % Model : x86_64 x86_64 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.29 % Memory : 8042.1875MB 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.29 % CPULimit : 1440 0.09/0.29 % WCLimit : 180 0.09/0.29 % DateTime : Mon Jul 3 10:28:07 EDT 2023 0.09/0.30 % CPUTime : 1.39/1.70 ============================== Prover9 =============================== 1.39/1.70 Prover9 (32) version 2009-11A, November 2009. 1.39/1.70 Process 17864 was started by sandbox2 on n021.cluster.edu, 1.39/1.70 Mon Jul 3 10:28:08 2023 1.39/1.70 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_17710_n021.cluster.edu". 1.39/1.70 ============================== end of head =========================== 1.39/1.70 1.39/1.70 ============================== INPUT ================================= 1.39/1.70 1.39/1.70 % Reading from file /tmp/Prover9_17710_n021.cluster.edu 1.39/1.70 1.39/1.70 set(prolog_style_variables). 1.39/1.70 set(auto2). 1.39/1.70 % set(auto2) -> set(auto). 1.39/1.70 % set(auto) -> set(auto_inference). 1.39/1.70 % set(auto) -> set(auto_setup). 1.39/1.70 % set(auto_setup) -> set(predicate_elim). 1.39/1.70 % set(auto_setup) -> assign(eq_defs, unfold). 1.39/1.70 % set(auto) -> set(auto_limits). 1.39/1.70 % set(auto_limits) -> assign(max_weight, "100.000"). 1.39/1.70 % set(auto_limits) -> assign(sos_limit, 20000). 1.39/1.70 % set(auto) -> set(auto_denials). 1.39/1.70 % set(auto) -> set(auto_process). 1.39/1.70 % set(auto2) -> assign(new_constants, 1). 1.39/1.71 % set(auto2) -> assign(fold_denial_max, 3). 1.39/1.71 % set(auto2) -> assign(max_weight, "200.000"). 1.39/1.71 % set(auto2) -> assign(max_hours, 1). 1.39/1.71 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.39/1.71 % set(auto2) -> assign(max_seconds, 0). 1.39/1.71 % set(auto2) -> assign(max_minutes, 5). 1.39/1.71 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.39/1.71 % set(auto2) -> set(sort_initial_sos). 1.39/1.71 % set(auto2) -> assign(sos_limit, -1). 1.39/1.71 % set(auto2) -> assign(lrs_ticks, 3000). 1.39/1.71 % set(auto2) -> assign(max_megs, 400). 1.39/1.71 % set(auto2) -> assign(stats, some). 1.39/1.71 % set(auto2) -> clear(echo_input). 1.39/1.71 % set(auto2) -> set(quiet). 1.39/1.71 % set(auto2) -> clear(print_initial_clauses). 1.39/1.71 % set(auto2) -> clear(print_given). 1.39/1.71 assign(lrs_ticks,-1). 1.39/1.71 assign(sos_limit,10000). 1.39/1.71 assign(order,kbo). 1.39/1.71 set(lex_order_vars). 1.39/1.71 clear(print_given). 1.39/1.71 1.39/1.71 % formulas(sos). % not echoed (530 formulas) 1.39/1.71 1.39/1.71 ============================== end of input ========================== 1.39/1.71 1.39/1.71 % From the command line: assign(max_seconds, 1440). 1.39/1.71 1.39/1.71 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.39/1.71 1.39/1.71 % Formulas that are not ordinary clauses: 1.39/1.71 1 (all V_R_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) -> (exists B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_y_2),V_R_2) & c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_z),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))))) # label(fact_tranclD2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 2 (all V_c_2 all T_a -c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 3 (all V_y_2 all V_x_2 all V_Y_2 all V_X_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_Y_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> (c_member(T_a,V_x_2,V_X_2) -> (c_member(T_a,V_y_2,V_Y_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> V_X_2 = V_Y_2))))))) # label(fact_quotient__eqI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 4 (all V_S_2 all V_R_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) -> c_Transitive__Closure_Ortrancl(T_a,V_R_2) = c_Transitive__Closure_Ortrancl(T_a,V_S_2)))) # label(fact_rtrancl__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 5 (all V_A_2 all V_r_2 all T_b all V_ba_2 all T_a ((exists B_x (c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_ba_2),V_r_2) & c_member(T_b,B_x,V_A_2))) <-> c_member(T_a,V_ba_2,c_Relation_OImage(T_b,T_a,V_r_2,V_A_2)))) # label(fact_Image__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 6 (exists B_L c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),B_L,c_Arrow__Order__Mirabelle_OLin)) # label(fact_linear__alt) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 7 v_b____ != v_a_H____ & v_b_H____ != v_a____ -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))) # label(fact_calculation_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 8 (all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_wf__acyclic) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 9 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Un__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 10 (all V_aa_2 all V_B_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2))) # label(fact_subset__insertI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 11 (all T_2 all T_1 (class_Groups_Ominus(T_1) -> class_Groups_Ominus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 12 (all V_x_2 all V_A_2 all V_y_2 all T_a (V_x_2 = V_y_2 | hBOOL(hAPP(V_A_2,V_x_2)) <-> hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)))) # label(fact_insert__code) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 13 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 14 (all V_s_2 all V_r_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a,V_r_2),c_Relation_OField(T_a,V_s_2)) = c_Relation_OField(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))) # label(fact_Field__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 15 (all V_A_2 all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_A_2)) # label(fact_Un__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 16 (all V_aa_2 all V_D_2 all V_C_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2),c_Set_Oinsert(T_a,V_aa_2,V_D_2)))) # label(fact_insert__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 17 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_ba_2,V_aa_2),V_r_2) <-> c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),c_Relation_Oconverse(T_b,T_a,V_r_2)))) # label(fact_converse__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 18 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d)))))) # label(fact_sup__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 19 (all V_r_2 all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,V_r_2) -> c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 20 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 21 (all V_A_2 all V_B_2 all V_c_2 all T_a ((-c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,V_A_2)) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnCI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 22 (all V_x all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x))))) # label(fact_le__supE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 23 (all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) = c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Id__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 24 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> V_A_2 = V_B_2))) # label(fact_equalityI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 25 (all V_x_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) | c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2)) # label(fact_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 26 (all T_b all T_a all B_M all B_R (c_Wellfounded_Owf(T_a,B_R) -> (all B_x hAPP(hAPP(B_M,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_R,B_x)),B_x) = hAPP(c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_x)))) # label(fact_tfl__wfrec) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 27 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_aa_2 = V_ba_2 -> (c_member(T_a,V_ba_2,V_A_2) -> c_member(T_a,V_aa_2,V_A_2)))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 28 (all V_A_2 all T_a V_A_2 = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_Un__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 29 (all V_r_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_a,V_r_2),c_Relation_ORange(T_a,T_a,V_r_2)) = c_Relation_OField(T_a,V_r_2)) # label(fact_Field__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 30 (all V_f_2 all V_r_2 all T_b all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)),V_r_2) <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oinv__image(T_b,T_a,V_r_2,V_f_2)))) # label(fact_in__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 31 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> (c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_IntI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 32 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_sup__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 33 (all V_L_2 (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_L_2),c_Arrow__Order__Mirabelle_OLin) <-> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin))) # label(fact_converse__in__Lin) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 34 (all V_c_2 all V_R_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_R_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),V_R_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))))) # label(fact_r__r__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 35 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 36 (all V_f_2 all V_R_2 all T_b all T_a c_Relation_Oinv__image(T_b,T_a,c_Relation_Oconverse(T_b,T_b,V_R_2),V_f_2) = c_Relation_Oconverse(T_a,T_a,c_Relation_Oinv__image(T_b,T_a,V_R_2,V_f_2))) # label(fact_converse__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 37 (all V_aa_2 all V_r_2 all T_b all V_ba_2 all T_a (c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_aa_2,V_ba_2),V_r_2) <-> c_member(T_a,V_ba_2,c_Relation_OImage(T_b,T_a,V_r_2,c_Set_Oinsert(T_b,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_Image__singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 38 (all V_Pa_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (hBOOL(hAPP(V_Pa_2,V_ba_2)) -> ((all B_y all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (hBOOL(hAPP(V_Pa_2,B_z)) -> hBOOL(hAPP(V_Pa_2,B_y)))))) -> hBOOL(hAPP(V_Pa_2,V_aa_2)))))) # label(fact_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 39 (all T_2 all T_1 (class_Lattices_Odistrib__lattice(T_1) -> class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 40 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 41 (all V_r_2 all T_b all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2) -> (all B_z (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2) -> B_y = B_z)))) <-> c_Relation_Osingle__valued(T_a,T_b,V_r_2))) # label(fact_single__valued__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 42 (all V_R_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) & V_ba_2 != V_aa_2 | V_ba_2 = V_aa_2)) # label(fact_rtranclD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 43 (all V_B_2 all V_A_2 all T_a c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2),V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Image__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 44 (all V_r_2 all T_b all T_a (V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ODomain(T_a,T_b,V_r_2))) # label(fact_Domain__empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 45 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 46 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Un__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 47 (all V_aa_2 all T_a c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_aa_2),c_Relation_OId(T_a))) # label(fact_IdI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 48 (all V_Pa_2 all V_B_2 all V_A_2 all T_a ((all B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_x (c_member(T_a,B_x,V_B_2) -> hBOOL(hAPP(V_Pa_2,B_x)))) & (all B_x (c_member(T_a,B_x,V_A_2) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ball__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 49 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Int__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 50 (all V_A_2 all V_y_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 51 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 52 (all V_L_2 all V_y_2 all V_x_2 (V_x_2 != V_y_2 -> (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_above__Lin) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 53 (all T_a c_Order__Relation_Olinear__order__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_lnear__order__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 54 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Opreorder__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2)) <-> c_Order__Relation_Opreorder__on(T_a,V_A_2,V_r_2))) # label(fact_preorder__on__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 55 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> V_B_2 = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)))) # label(fact_Diff__partition) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 56 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 57 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a)) = V_x)) # label(fact_sup__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 58 (all V_s_2 all V_r_2 all V_b_Ha_2 all V_a_Ha_2 all V_ba_2 all V_aa_2 all T_b all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_a_Ha_2),V_r_2) | V_a_Ha_2 = V_aa_2 & c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_ba_2,V_b_Ha_2),V_s_2) <-> c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),c_Product__Type_OPair(T_a,T_b,V_a_Ha_2,V_b_Ha_2)),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 59 (all T_a c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) # label(fact_trancl__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 60 (all V_aa_2 all V_ba_2 all T_a (c_member(T_a,V_ba_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> V_aa_2 = V_ba_2)) # label(fact_singletonE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 61 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_z,V_x)))) # label(fact_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 62 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2)) # label(fact_Int__lower2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 63 (all V_B_2 all V_A_2 all V_x_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) & c_member(T_a,V_x_2,V_B_2))) # label(fact_insert__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 64 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> c_member(T_a,V_x_2,V_A_2)))) # label(fact_refl__onD1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 65 (all V_s_2 all V_r_2 all T_a all T_b c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Oconverse(T_b,T_a,V_r_2),c_Relation_Oconverse(T_b,T_a,V_s_2)) = c_Relation_Oconverse(T_b,T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_r_2,V_s_2))) # label(fact_converse__Int) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 66 (all V_x_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_x_2,V_A_2) -> c_member(T_a,V_x_2,V_B_2)))) # label(fact_in__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 67 (all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2) # label(fact_Un__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 68 (all V_ba_2 all V_aa_2 all V_r_2 all T_a (c_Order__Relation_Opartial__order__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_member(T_a,V_aa_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(T_a,V_ba_2,c_Relation_OField(T_a,V_r_2)) -> (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_ba_2 = V_aa_2))))) # label(fact_Partial__order__eq__Image1__Image1__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 69 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__Diff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 70 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> -(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)))) # label(fact_equalityE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 71 (all V_r_2 all V_zb_2 all V_za_2 all V_xb_2 all V_xa_2 all T_b all T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2) != c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2) -> -(all B_a all B_b (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,B_a,B_b)),V_r_2) -> -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))))))) # label(fact_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 72 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = V_x)) # label(fact_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 73 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 74 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> (c_Relation_Osingle__valued(T_a,T_b,V_s_2) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2)))) # label(fact_single__valued__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 75 (all V_A_2 all V_c_2 all T_a (c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2)) -> -(all B_x (c_member(T_a,B_x,V_A_2) -> V_c_2 != c_Product__Type_OPair(T_a,T_a,B_x,B_x))))) # label(fact_Id__onE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 76 (all T_a c_Relation_Oantisym(T_a,c_Relation_OId(T_a))) # label(fact_antisym__Id) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 77 (all V_B_2 all V_A_2 all V_aa_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_insert__inter__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 78 (all T_a all V_B_2 all V_x_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_x_2)) -> (hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))))) # label(fact_inf1I) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 79 (all V_R_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) -> (exists B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) & c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_z),V_R_2))))) # label(fact_tranclD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 80 (all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (exists B_x (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),B_x,c_Arrow__Order__Mirabelle_OLin) & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),B_x))))) # label(fact_complete__Lin) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 81 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 82 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> ((all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 83 (all V_r_H_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_r_H_2)))) # label(fact_wf__Int1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 84 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__le1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 85 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> (-hBOOL(hAPP(V_A_2,V_x_2)) -> hBOOL(hAPP(V_B_2,V_x_2))))) # label(fact_sup1E) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 86 (all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a))) # label(fact_single__valued__Id) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 87 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Opartial__order__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2)) <-> c_Order__Relation_Opartial__order__on(T_a,V_A_2,V_r_2))) # label(fact_partial__order__on__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 88 (all V_A_2 all V_aa_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_Set_Oinsert(T_a,V_aa_2,V_A_2)) # label(fact_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 89 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))))) # label(fact_inf__greatest) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 90 (all V_ba_2 all V_aa_2 all V_r_2 all T_a (c_Relation_Orefl__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_Relation_Oantisym(T_a,V_r_2) -> (c_member(T_a,V_aa_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(T_a,V_ba_2,c_Relation_OField(T_a,V_r_2)) -> (V_ba_2 = V_aa_2 <-> c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))))) # label(fact_Refl__antisym__eq__Image1__Image1__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 91 (all V_A_2 all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_single__valued__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 92 (all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) <-> (all B_x c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_wf__acc__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 93 (all V_ba_2 all V_aa_2 all V_L_2 (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),V_L_2) -> -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_ba_2,V_aa_2),V_L_2)))) # label(fact_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 94 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 95 (all V_r_2 all V_x_2 all V_y_2 all T_a (c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2)) <-> c_Wellfounded_Oacyclic(T_a,V_r_2) & -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_acyclic__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 96 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 97 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))) # label(fact_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 98 (all V_a2_2 all V_a1_2 all V_Fa_2 all V_R_2 all T_b all T_a (c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2,V_a2_2) <-> (exists B_g (V_a2_2 = hAPP(hAPP(V_Fa_2,B_g),V_a1_2) & (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(B_g,B_z)))))))) # label(fact_wfrec__rel_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 99 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 100 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a,V_r_2),c_Relation_OField(T_a,V_s_2)))) # label(fact_mono__Field) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 101 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c)))) # label(fact_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 102 (all V_B_2 all T_a all V_x_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_x_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))) # label(fact_sup1I1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 103 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> (V_y_2 != V_x_2 & (V_aa_2 = V_y_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_ba_2),V_L_2)) & (V_aa_2 != V_y_2 -> (V_aa_2 != V_x_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)) & (V_x_2 = V_aa_2 -> V_ba_2 = V_y_2 | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_ba_2,V_y_2),V_L_2))) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2)))))) # label(fact_in__below) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 104 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> V_B_2 = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 105 (all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_trancl_Or__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 106 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_subset__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 107 (all V_r_2 all T_a ((all B_x c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)) <-> c_Nitpick_Orefl_H(T_a,V_r_2))) # label(fact_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 108 (all V_y_2 all V_x_2 (-hBOOL(hAPP(c_fequal(V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 109 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b))))) # label(fact_le__infE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 110 (all V_A_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_OId__on(T_a,V_A_2)) <-> c_member(T_a,V_x_2,V_A_2) & V_x_2 = V_y_2)) # label(fact_Id__on__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 111 (all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_trancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 112 (all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_quotient__is__empty2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 113 (all V_r_2 all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,V_r_2) -> c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_r__into__trancl_H) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 114 (all V_A_2 all T_a c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2) # label(fact_Domain__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 115 (all T_b all T_a all V_Pa_2 ((all B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> (all B_a all B_b hBOOL(hAPP(V_Pa_2,c_Product__Type_OPair(T_a,T_b,B_a,B_b)))))) # label(fact_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 116 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Diff__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 117 (all T_a c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_refl__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 118 (all T_a c_Relation_OId(T_a) = c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_rtrancl__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 119 (all V_aa_2 all V_ba_2 all T_a (V_aa_2 = V_ba_2 <-> c_member(T_a,V_ba_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 120 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_x))) # label(fact_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 121 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_b all T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2) -> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_r_2) -> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_z_2),V_r_2) -> V_z_2 = V_y_2)))) # label(fact_single__valuedD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 122 (all V_ba_2 all V_aa_2 all V_f1_2 all T_a all T_c all T_b hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2) = c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,c_Product__Type_OPair(T_b,T_c,V_aa_2,V_ba_2))) # label(fact_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 123 (all V_A_2 all T_a ((all B_x -c_member(T_a,B_x,V_A_2)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 124 (all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_wf__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 125 (all V_ba_2 all V_B_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,V_B_2) -> c_member(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,V_B_2)))) # label(fact_insertI2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 126 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),c_Relation_Oconverse(T_b,T_a,V_r_2)) -> c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_ba_2,V_aa_2),V_r_2))) # label(fact_converseD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 127 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 128 (all V_A_2 all V_x_2 all T_a (c_member(T_a,V_x_2,V_A_2) <-> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 129 (all V_X_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,V_X_2),V_X_2) -> c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_X_2) = V_X_2)) # label(fact_Image__closed__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 130 (all V_c_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((c_member(T_a,V_c_2,V_A_2) -> -c_member(T_a,V_c_2,V_B_2)) -> -(-c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 131 (all V_x_2 all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> (c_member(T_a,V_x_2,V_B_2) <-> c_member(T_a,V_x_2,V_A_2)))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 132 (all T_b all V_aa_2 all V_x_2 all T_a all B_f all B_R (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_aa_2),B_R) -> hAPP(c_Recdef_Ocut(T_a,T_b,B_f,B_R,V_aa_2),V_x_2) = hAPP(B_f,V_x_2))) # label(fact_tfl__cut__apply) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 133 (all V_B_2 all V_A_2 all V_R_2 all T_a all T_b c_Relation_OImage(T_b,T_a,V_R_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_R_2,V_B_2))) # label(fact_Image__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 134 (all V_c_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_subsetD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.71 135 (all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2)) <-> c_Relation_Orefl__on(T_a,V_A_2,V_r_2))) # label(fact_refl__on__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 136 (all V_y_2 all V_x_2 all V_Y_2 all V_X_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_Y_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> (c_member(T_a,V_x_2,V_X_2) -> (c_member(T_a,V_y_2,V_Y_2) -> (V_Y_2 = V_X_2 <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)))))))) # label(fact_quotient__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 137 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> (c_Relation_Oantisym(T_a,V_s_2) -> c_Relation_Oantisym(T_a,V_r_2)))) # label(fact_antisym__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 138 (all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x) = V_x)) # label(fact_sup__idem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 139 (all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (class_Groups_Ominus(T_a) -> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 140 (all T_a c_Order__Relation_Opreorder__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_preorder__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 141 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d)))))) # label(fact_inf__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 142 (all V_s_2 all V_r_2 all T_a all T_b c_Relation_Oconverse(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_r_2,V_s_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Oconverse(T_b,T_a,V_r_2),c_Relation_Oconverse(T_b,T_a,V_s_2))) # label(fact_converse__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 143 (all V_P_Ha_2 all V_Pa_2 all V_b_Ha_2 all V_a_Ha_2 all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_2 -> (V_a_Ha_2 != V_b_Ha_2 -> (V_b_Ha_2 != V_aa_2 -> (V_ba_2 != V_a_Ha_2 -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf) -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf) -> ((all B_i (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i)))) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))))))))))) # label(fact__C2_C) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 144 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> c_member(T_a,V_y_2,V_A_2)))) # label(fact_refl__onD2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 145 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Int__lower1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 146 (all V_r_2 all T_b all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2) -> (all B_z (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2) -> B_z = B_y)))) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2))) # label(fact_single__valuedI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 147 (all V_r_2 all T_a c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))) # label(fact_trancl__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 148 (all V_A_2 all T_a all V_y_2 all V_x_2 (V_x_2 = V_y_2 -> (c_member(T_a,V_y_2,V_A_2) <-> c_member(T_a,V_x_2,V_A_2)))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 149 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2),V_z_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_z_2)))) # label(fact_le__sup__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 150 (all V_A_2 all T_a c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2))) # label(fact_refl__on__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 151 (all V_r_2 all T_a (c_Relation_Oantisym(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))) <-> c_Relation_Oantisym(T_a,V_r_2))) # label(fact_antisym__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 152 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 153 (all V_aa_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_aa_2,V_A_2) -> c_member(T_a,V_aa_2,c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))) # label(fact_equiv__class__self) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 154 (all V_r_2 all V_x_2 all T_a c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Equiv__Relations_Oquotient(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) # label(fact_singleton__quotient) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 155 (all V_ba_2 all V_B_2 all V_aa_2 all T_a ((-c_member(T_a,V_aa_2,V_B_2) -> V_ba_2 = V_aa_2) -> c_member(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,V_B_2)))) # label(fact_insertCI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 156 (all T_a c_Relation_OId(T_a) = c_Relation_Oconverse(T_a,T_a,c_Relation_OId(T_a))) # label(fact_converse__Id) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 157 (all T_a all V_R_2 all T_b all V_Pa_2 ((all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)))) -> c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2)))) # label(fact_wf__same__fst) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 158 (all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a) = V_a)) # label(fact_inf_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 159 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_aa_2 = V_ba_2 -> (c_member(T_a,V_aa_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Relation_OId__on(T_a,V_A_2))))) # label(fact_Id__on__eqI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 160 (all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) <-> (all B_x all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2) -> B_y = B_x))))) # label(fact_antisym__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 161 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x))))) # label(fact_le__supI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 162 (all V_f_2 all T_a c_Wellfounded_Owf(T_a,c_Wellfounded_Omeasure(T_a,V_f_2))) # label(fact_wf__measure) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 163 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))) # label(fact_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 164 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) <-> c_member(T_a,V_c_2,V_A_2) & c_member(T_a,V_c_2,V_B_2))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 165 (all V_y_2 all V_x_2 all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> V_y_2 != V_x_2))) # label(fact_irrefl__trancl__rD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 166 (all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_equalityD2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 167 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> V_x = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x))) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 168 (all V_r_2 all V_s_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_s_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Wellfounded_Oacyclic(T_a,V_r_2)))) # label(fact_acyclic__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 169 (all V_r_2 all T_b all T_a c_Relation_ORange(T_b,T_a,V_r_2) = c_Relation_ODomain(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_r_2))) # label(fact_Domain__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 170 (all V_A_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Int__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 171 (all V_i_2 all V_Fa_2 (c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) <-> (all B_x (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x,c_Arrow__Order__Mirabelle_OProf) -> hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2))))) # label(fact_dictator__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 172 (all V_r_H_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_H_2,V_r_2)))) # label(fact_wf__Int2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 173 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),V_r_2) -> c_member(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)))) # label(fact_DomainI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 174 (all V_aa_2 all V_f_2 all V_r2_2 all T_c all T_b all V_r1_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) -> (c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) -> (c_member(T_a,V_aa_2,V_A_2) -> c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_aa_2)))))) # label(fact_congruent2__implies__congruent) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 175 (all V_r_2 all T_a c_Relation_OField(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)) = c_Relation_OField(T_a,V_r_2)) # label(fact_Field__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 176 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 177 (all V_y_2 all V_x_2 all V_L_2 (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> (V_x_2 != V_y_2 -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_y_2,V_x_2),V_L_2) <-> -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2))))) # label(fact_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 178 (all V_Pa_2 all V_r_2 all V_by_2 all V_bx_2 all V_ay_2 all V_ax_2 all T_b all T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) -> ((all B_a all B_b all B_aa all B_ba (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba)),V_r_2) -> (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)))))) # label(fact_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 179 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_x_2,V_A_2) -> (c_member(T_a,V_y_2,V_A_2) -> (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_y_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)))))) # label(fact_eq__equiv__class__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 180 (all V_aa_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_aa_2),V_r_2))) # label(fact_wf__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 181 (all V_s_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_Wellfounded_Owf(T_a,V_s_2) -> (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_a,V_r_2),c_Relation_ORange(T_a,T_a,V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) -> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)))))) # label(fact_wf__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 182 (all V_r_2 all T_a c_Transitive__Closure_Otrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2)) # label(fact_trancl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 183 (all V_x_2 all V_aa_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_x_2),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_aa_2),V_r_2)))) # label(fact_wf__not__sym) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 184 (all V_r_2 all T_a ((all B_Q ((exists B_x c_member(T_a,B_x,B_Q)) -> (exists B_x ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2) -> -c_member(T_a,B_y,B_Q))) & c_member(T_a,B_x,B_Q))))) <-> c_Wellfounded_Owf(T_a,V_r_2))) # label(fact_wf__eq__minimal) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 185 (all V_A_2 all V_ba_2 all V_aa_2 all V_r_2 all T_a (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_ba_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2))))) # label(fact_eq__equiv__class) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 186 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Diff__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 187 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 188 (all V_R_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__reflcl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 189 (all V_Fa_2 (c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) <-> (all B_x (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x,c_Arrow__Order__Mirabelle_OProf) -> (all B_xa (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_xa,c_Arrow__Order__Mirabelle_OProf) -> (all B_a all B_b ((all B_i (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(B_x,B_i)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(B_xa,B_i)))) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(V_Fa_2,B_x)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(V_Fa_2,B_xa))))))))))) # label(fact_IIA__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 190 (all V_y_2 all V_R_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,c_Relation_ODomain(T_a,T_a,V_R_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) <-> V_y_2 = V_x_2))) # label(fact_Not__Domain__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 191 (all V_B_2 all V_A_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 192 (all V_ba_2 all V_r_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,c_Wellfounded_Oacc(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_aa_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(T_a,V_ba_2,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc__downwards) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 193 (all V_ba_2 all V_aa_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))) # label(fact_equiv__class__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 194 (all V_r_2 all V_z_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),V_r_2) -> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_y),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))))) # label(fact_converse__tranclE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 195 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))))) # label(fact_distrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 196 (all V_Pa_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (hBOOL(hAPP(V_Pa_2,V_aa_2)) -> ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,B_y),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2) -> (hBOOL(hAPP(V_Pa_2,B_y)) -> hBOOL(hAPP(V_Pa_2,B_z))))))) -> hBOOL(hAPP(V_Pa_2,V_ba_2)))))) # label(fact_rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 197 (all V_A_2 all T_a c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a),V_A_2) = V_A_2) # label(fact_Image__Id) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 198 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c))) # label(fact_inf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 199 (all V_R_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_R_2)) -> -(all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_x_2),V_R_2) -> c_member(T_a,B_z,c_Wellfounded_Oacc(T_a,V_R_2)))))) # label(fact_not__acc__down) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 200 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Olattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Olattice) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 201 (all V_aa_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_aa_2),V_r_2))) # label(fact_wf__not__refl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 202 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2)))) # label(fact_Range__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 203 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) # label(fact_empty__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 204 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__ge2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 205 (all V_B_2 all V_A_2 all T_b all T_a c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2))) # label(fact_Domain__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 206 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__rtrancl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 207 (all V_r_2 all V_ba_2 all V_aa_2 all T_a all T_b c_Set_Oinsert(T_a,V_ba_2,c_Relation_ORange(T_b,T_a,V_r_2)) = c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_aa_2,V_ba_2),V_r_2))) # label(fact_Range__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 208 (all V_r_2 all T_b all V_aa_2 all T_a (c_member(T_a,V_aa_2,c_Relation_ORange(T_b,T_a,V_r_2)) <-> (exists B_y c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_y,V_aa_2),V_r_2)))) # label(fact_Range__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 209 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 210 (all V_A_2 all V_B_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__upper2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 211 (all V_r_2 all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2) -> B_x = B_y))) -> c_Relation_Oantisym(T_a,V_r_2))) # label(fact_antisymI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 212 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 213 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2)))) # label(fact_Domain__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 214 (all T_a c_Order__Relation_Opartial__order__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_partial__order__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 215 (all V_r_2 all V_x_2 all T_a ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2) -> c_member(T_a,B_y,c_Wellfounded_Oacc(T_a,V_r_2)))) -> c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)))) # label(fact_acc_OaccI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 216 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> hBOOL(hAPP(V_B_2,V_x_2)))) # label(fact_inf1D2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 217 (all V_R_2 all T_a c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__trancl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 218 (all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Diff__idemp) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 219 (all V_A_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 220 (all T_a all V_R_2 all V_y_2 all V_y_H_2 all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_y_H_2,V_y_2),hAPP(V_R_2,V_x_2)) -> c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_H_2),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2)),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2))))) # label(fact_same__fstI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 221 (all V_f_2 all T_b all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_b,c_Relation_Oinv__image(T_a,T_b,V_r_2,V_f_2)))) # label(fact_wf__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 222 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) <-> c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_y_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) & c_member(T_a,V_y_2,V_A_2) & c_member(T_a,V_x_2,V_A_2)))) # label(fact_equiv__class__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 223 (all V_f_2 all V_R_2 all T_a (c_Wellfounded_Owf(T_a,V_R_2) -> c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))) # label(fact_wf__mlex) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 224 (all V_P_Ha_2 all V_Pa_2 all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_2 -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf) -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf) -> ((all B_i (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_ba_2,V_aa_2),hAPP(V_P_Ha_2,B_i)))) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_ba_2,V_aa_2),hAPP(v_F,V_P_Ha_2)))))))) # label(fact__C3_C) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 225 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 226 (all V_A_2 all V_r_2 all T_b all V_ba_2 all T_a (c_member(T_a,V_ba_2,c_Relation_OImage(T_b,T_a,V_r_2,V_A_2)) -> -(all B_x (c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_ba_2),V_r_2) -> -c_member(T_b,B_x,V_A_2))))) # label(fact_ImageE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 227 (all V_r_2 all T_a all T_b c_Relation_ODomain(T_a,T_b,V_r_2) = c_Relation_ORange(T_b,T_a,c_Relation_Oconverse(T_a,T_b,V_r_2))) # label(fact_Range__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 228 (all T_a all V_A_2 all V_x_2 all V_B_2 ((-hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(V_A_2,V_x_2))) -> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))) # label(fact_sup1CI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 229 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z))) # label(fact_inf__assoc) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 230 (all V_r_2 all T_a all T_b c_Relation_ORange(T_b,T_a,V_r_2) = c_Relation_ODomain(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_r_2))) # label(fact_Range__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 231 (all V_s_2 all V_r_2 all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_s_2))))) # label(fact_trancl__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 232 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_rtrancl__into__trancl1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 233 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Int__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 234 (all V_y_2 all V_x_2 all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> (V_x_2 = c_Orderings_Obot__class_Obot(T_a) & c_Orderings_Obot__class_Obot(T_a) = V_y_2 <-> c_Orderings_Obot__class_Obot(T_a) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)))) # label(fact_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 235 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 236 (all V_P_Ha_2 all V_Pa_2 all V_c_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_ba_2 != V_c_2 -> (V_aa_2 != V_c_2 -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf) -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf) -> ((all B_i (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_ba_2,V_c_2),hAPP(V_P_Ha_2,B_i)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)))) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_ba_2,V_c_2),hAPP(v_F,V_P_Ha_2)))))))))) # label(fact__C4_C) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 237 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 238 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)) <-> c_Relation_Oirrefl(T_a,V_r_2))) # label(fact_irrefl__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 239 (all V_z all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x))))) # label(fact_sup__least) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 240 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 241 (all V_P_Ha_2 all V_Pa_2 all V_b_Ha_2 all V_a_Ha_2 all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_2 -> (V_a_Ha_2 != V_b_Ha_2 -> (V_b_Ha_2 != V_aa_2 -> (V_ba_2 != V_a_Ha_2 -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf) -> (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf) -> ((all B_i (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i)))) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2)) -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))))))))))) # label(fact__C1_C) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 242 (all V_r_2 all V_A_2 all T_a (c_Wellfounded_Owf(T_a,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))) & c_Order__Relation_Olinear__order__on(T_a,V_A_2,V_r_2) <-> c_Order__Relation_Owell__order__on(T_a,V_A_2,V_r_2))) # label(fact_well__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 243 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2))))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.72 244 (all V_b_H all V_a_H all V_b all V_a all T_b all T_a (c_Product__Type_OPair(T_a,T_b,V_a,V_b) = c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H) -> -(V_a = V_a_H -> V_b != V_b_H))) # label(fact_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 245 (all V_A_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2)) # label(fact_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 246 (all V_B_2 all V_A_2 all V_C_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_Int__greatest) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 247 (all V_B_2 all V_A_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_subset__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 248 (all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) <-> c_Relation_Oantisym(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))) # label(fact_antisym__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 249 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_equalityD1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 250 (all V_A_2 all T_a c_Relation_OId__on(T_a,V_A_2) = c_Relation_Oconverse(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_converse__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 251 (all T_b all T_a c_Relation_ODomain(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Domain__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 252 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 253 (all V_B_2 all V_C_2 all V_aa_2 all T_a ((-c_member(T_a,V_aa_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) & (c_member(T_a,V_aa_2,V_C_2) -> c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2)))) # label(fact_Int__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 254 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 255 (all V_a all V_b all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_le__supI2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 256 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Un__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 257 (all V_x_2 all V_L_2 (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_x_2),c_Arrow__Order__Mirabelle_OLin))) # label(fact_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 258 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> (-c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_UnE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 259 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> V_A_2 = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))))) # label(fact_double__diff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 260 (all V_A_2 all T_a c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_antisym__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 261 (all V_aa_2 all V_H_2 all T_b all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_r_2,V_aa_2)),V_aa_2) = hAPP(c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_aa_2))) # label(fact_wfrec) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 262 (all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)))) # label(fact_Un__least) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 263 (all V_Pa_2 all V_r_2 all V_by_2 all V_bx_2 all V_ay_2 all V_ax_2 all T_b all T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) -> ((all B_a all B_b (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,B_a,B_b)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (all B_aa all B_ba (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba)),V_r_2) -> (hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)))))) # label(fact_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 264 (all V_p_2 all V_r_2 all T_a (c_Wellfounded_OwfP(T_a,V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_p_2,V_r_2) -> c_Wellfounded_OwfP(T_a,V_p_2)))) # label(fact_wfP__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 265 (all V_r_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__converseD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 266 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2)) # label(fact_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 267 v_a____ = v_b_H____ & v_a_H____ != v_b____ -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))) # label(fact_calculation_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 268 (all V_B_2 all V_aa_2 all T_a c_member(T_a,V_aa_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2))) # label(fact_insertI1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 269 (all V_R_2 all T_a all V_y_2 all V_x_2 all V_f_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_R_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))))) # label(fact_mlex__leq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 270 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__upper1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 271 (all V_r_2 all V_ba_2 all T_b all V_A_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,V_A_2) -> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),V_r_2) -> c_member(T_b,V_ba_2,c_Relation_OImage(T_a,T_b,V_r_2,V_A_2))))) # label(fact_rev__ImageI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 272 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 273 (all V_r_2 all V_A_2 all V_X_2 all T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> -(all B_x (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,B_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_X_2 -> -c_member(T_a,B_x,V_A_2))))) # label(fact_quotientE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 274 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_y = V_x)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 275 (all V_r_2 all V_aa_2 all V_ba_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_aa_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(T_a,V_aa_2,c_Wellfounded_Oacc(T_a,V_r_2)) -> c_member(T_a,V_ba_2,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc__downwards__aux) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 276 (all V_A_2 all V_aa_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_Set_Oinsert(T_a,V_aa_2,V_A_2)) # label(fact_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 277 (all V_g_2 all V_x_2 all V_r_2 all V_f_2 all T_b all T_a ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2) -> hAPP(V_g_2,B_y) = hAPP(V_f_2,B_y))) <-> c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_x_2) = c_Recdef_Ocut(T_a,T_b,V_g_2,V_r_2,V_x_2))) # label(fact_cuts__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 278 (all V_b_Ha_2 all V_a_Ha_2 all V_ba_2 all V_aa_2 all T_b all T_a (V_a_Ha_2 = V_aa_2 & V_b_Ha_2 = V_ba_2 <-> c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2) = c_Product__Type_OPair(T_a,T_b,V_a_Ha_2,V_b_Ha_2))) # label(fact_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 279 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Orderings_Obot__class_Obot(T_a) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Obot__class_Obot(T_a),V_x))) # label(fact_inf__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 280 (all V_ba_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_ba_2,V_B_2)))) # label(fact_subset__insertI2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 281 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_aa_2,V_ba_2)) -> hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2))))) # label(fact_curryE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 282 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_A_2))) # label(fact_IntD1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 283 (all V_A_2 all V_C_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2)) # label(fact_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 284 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> V_A_2 = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 285 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> -(hBOOL(hAPP(V_A_2,V_x_2)) -> -hBOOL(hAPP(V_B_2,V_x_2))))) # label(fact_inf1E) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 286 (all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = V_B_2) # label(fact_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 287 (all V_A_2 all V_A_H_2 all V_r_2 all V_r_H_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_H_2,V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Relation_OImage(T_a,T_b,V_r_H_2,V_A_H_2),c_Relation_OImage(T_a,T_b,V_r_2,V_A_2))))) # label(fact_Image__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 288 (all V_r_2 all V_x_2 all V_y_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))))) # label(fact_rtrancl__converseI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 289 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x) = V_x)) # label(fact_sup__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 290 (all V_r_2 all T_a all T_b c_Relation_Oconverse(T_b,T_a,c_Relation_Oconverse(T_a,T_b,V_r_2)) = V_r_2) # label(fact_converse__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 291 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Un__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 292 (all V_r_2 all V_A_2 all V_x_2 all T_a (c_member(T_a,V_x_2,V_A_2) -> c_member(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)))) # label(fact_quotientI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 293 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> -(c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_DiffE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 294 (all V_ba_2 all V_aa_2 all V_r_2 all T_a (c_Order__Relation_Opreorder__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_member(T_a,V_aa_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(T_a,V_ba_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_aa_2),V_r_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))))) # label(fact_subset__Image1__Image1__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 295 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 296 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> V_x = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 297 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Opartial__order__on(T_a,V_A_2,V_r_2) <-> c_Order__Relation_Opreorder__on(T_a,V_A_2,V_r_2) & c_Relation_Oantisym(T_a,V_r_2))) # label(fact_partial__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 298 (all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_subset__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 299 (all V_B_2 all V_A_2 all V_r_2 all T_a (c_Order__Relation_Opreorder__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Relation_OField(T_a,V_r_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Relation_OField(T_a,V_r_2)) -> ((all B_x (c_member(T_a,B_x,V_A_2) -> (exists B_xa (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2) & c_member(T_a,B_xa,V_B_2))))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,V_A_2),c_Relation_OImage(T_a,T_a,V_r_2,V_B_2))))))) # label(fact_subset__Image__Image__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 300 (all T_a c_Order__Relation_Owell__order__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_well__order__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 301 (all V_C_2 all V_B_2 all V_aa_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 302 (all V_B_2 all V_A_2 all V_R_2 all T_b all T_a (c_Relation_Osingle__valued(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_R_2)) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_R_2,V_B_2)) = c_Relation_OImage(T_b,T_a,V_R_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Image__Int__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 303 (all V_rb_2 all T_b all V_ra_2 all T_a (c_Wellfounded_Owf(T_a,V_ra_2) -> (c_Wellfounded_Owf(T_b,V_rb_2) -> c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2))))) # label(fact_wf__lex__prod) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 304 (all V_ba_2 all V_aa_2 all T_a (c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) -> V_aa_2 = V_ba_2)) # label(fact_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 305 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 306 (all V_r_2 all T_a all T_b (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) = V_r_2 <-> c_Relation_ORange(T_b,T_a,V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Range__empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 307 (all V_A_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,V_A_2) -> V_A_2 = c_Set_Oinsert(T_a,V_aa_2,V_A_2))) # label(fact_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 308 (all V_A_2 all T_a all V_x_2 all V_B_2 (hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))) # label(fact_sup1I2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 309 (all V_s_2 all V_B_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_Relation_Orefl__on(T_a,V_B_2,V_s_2) -> c_Relation_Orefl__on(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))))) # label(fact_refl__on__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 310 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a))) # label(fact_sup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 311 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)))) # label(fact_sup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 312 (all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2) = V_y_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_le__iff__sup) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 313 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_aa_2,V_ba_2)) -> hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2))))) # label(fact_curryD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 314 (all T_a all T_b c_Relation_ORange(T_b,T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Range__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 315 (all V_Q_2 all T_a all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 316 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2)),c_Relation_ORange(T_b,T_a,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Range__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 317 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2)))) # label(fact_Domain__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 318 (all V_r_2 all T_a c_Relation_ODomain(T_a,T_a,V_r_2) = c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))) # label(fact_trancl__domain) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 319 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_2 -> (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_aa_2,V_ba_2)) <-> V_x_2 != V_y_2 & (V_x_2 != V_ba_2 -> (V_ba_2 != V_y_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)) & (V_y_2 = V_ba_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_aa_2),V_L_2) | V_x_2 = V_aa_2)) & (V_x_2 = V_ba_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_y_2),V_L_2)))))) # label(fact_in__above) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 320 (all V_L_2 all V_y_2 all V_x_2 (V_y_2 != V_x_2 -> (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_below__Lin) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 321 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> -(c_member(T_a,V_c_2,V_A_2) -> -c_member(T_a,V_c_2,V_B_2)))) # label(fact_IntE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 322 (all V_aa_2 all V_ba_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) -> (c_member(T_a,V_ba_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2))))) # label(fact_subset__equiv__class) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 323 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 324 (all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a) = V_a)) # label(fact_sup_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 325 (all V_B_2 all V_A_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,V_A_2) -> (-c_member(T_a,V_x_2,V_B_2) -> (V_B_2 = V_A_2 <-> c_Set_Oinsert(T_a,V_x_2,V_B_2) = c_Set_Oinsert(T_a,V_x_2,V_A_2))))) # label(fact_insert__ident) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 326 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_sup__assoc) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 327 (all V_x all V_y all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_y))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 328 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__le2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 329 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> (-c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_DiffI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 330 (all V_ba_2 all V_aa_2 all T_a (V_ba_2 = V_aa_2 <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Relation_OId(T_a)))) # label(fact_pair__in__Id__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 331 (all V_B_2 all V_C_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,V_C_2) -> c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2))) # label(fact_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 332 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 333 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))))) # label(fact_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 334 (all V_aa_2 all T_a all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) -> -c_member(T_a,V_aa_2,V_A_2))) # label(fact_equals0D) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 335 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_z,V_x)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z),V_x))) # label(fact_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 336 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),V_r_2) -> c_member(T_b,V_ba_2,c_Relation_ORange(T_a,T_b,V_r_2)))) # label(fact_RangeI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 337 (all V_r_2 all V_aa_2 all T_a c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_aa_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 338 (all V_S_2 all V_R_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) | c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_S_2)) -> c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))))) # label(fact_in__rtrancl__UnI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 339 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_Transitive__Closure_Otrancl__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 340 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 341 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_fequal(V_x_2),V_y_2)) | V_y_2 != V_x_2)) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 342 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_x_2,V_A_2) -> (c_member(T_a,V_y_2,V_A_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) <-> c_Equiv__Relations_Oquotient(T_a,c_Set_Oinsert(T_a,V_y_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Equiv__Relations_Oquotient(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2)))))) # label(fact_eq__equiv__class__iff2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 343 (all V_ba_2 all V_aa_2 all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_aa_2),V_r_2) -> V_aa_2 = V_ba_2)))) # label(fact_antisymD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 344 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 345 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (V_ba_2 = V_aa_2 | c_member(T_a,V_aa_2,V_A_2) <-> c_member(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,V_A_2)))) # label(fact_insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 346 (all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x_2,V_y_2)))) # label(fact_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 347 (all V_x all T_a (class_Orderings_Obot(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Obot__class_Obot(T_a),V_x))) # label(fact_bot__least) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 348 (all B_i (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,B_i)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i)))) # label(fact_A_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 349 (all V_aa_2 all V_H_2 all V_r_2 all T_b all T_a all V_f_2 (V_f_2 = c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2) -> (c_Wellfounded_Owf(T_a,V_r_2) -> hAPP(V_f_2,V_aa_2) = hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_aa_2)),V_aa_2)))) # label(fact_def__wfrec) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 350 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2)) <-> V_x_2 != V_z_2 & (V_z_2 != V_y_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)) & (V_z_2 = V_y_2 -> V_x_2 != V_y_2))) # label(fact_in__mktop) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 351 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 352 (all V_g_2 all V_Fa_2 all T_b all V_R_2 all V_x_2 all T_a ((all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_x_2),V_R_2) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(V_g_2,B_z)))) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2,hAPP(hAPP(V_Fa_2,V_g_2),V_x_2)))) # label(fact_wfrec__rel_Ointros) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 353 (all V_r_2 all V_x_2 all V_y_2 all T_a (c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2)) <-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) & c_Wellfounded_Owf(T_a,V_r_2))) # label(fact_wf__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 354 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))) # label(fact_sup__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 355 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 356 (all V_R_2 all T_a all T_b c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_OImage(T_b,T_a,V_R_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_Image__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 357 (all V_B_2 all V_A_2 all V_x_2 all T_a (c_member(T_a,V_x_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_member(T_a,V_x_2,V_B_2)))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 358 (all V_d_2 all V_c_2 all V_ba_2 all V_aa_2 all T_a (V_ba_2 = V_c_2 & V_d_2 = V_aa_2 | V_d_2 = V_ba_2 & V_c_2 = V_aa_2 <-> c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Set_Oinsert(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 359 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c)))) # label(fact_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 360 (all V_y_2 all V_x_2 all T_a (c_member(T_a,V_x_2,c_fequal(V_y_2)) <-> V_x_2 = V_y_2)) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 361 (all V_r_2 all V_A_2 all T_a (c_Relation_Ototal__on(T_a,V_A_2,V_r_2) <-> c_Relation_Ototal__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2)))) # label(fact_total__on__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 362 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.39/1.73 363 (all V_Pa_2 all V_B_2 all V_A_2 all T_a ((exists B_x (c_member(T_a,B_x,V_A_2) & hBOOL(hAPP(V_Pa_2,B_x)))) | (exists B_x (c_member(T_a,B_x,V_B_2) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x (hBOOL(hAPP(V_Pa_2,B_x)) & c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))))) # label(fact_bex__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 364 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2))) # label(fact_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 365 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 366 (all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,c_Relation_OId(T_a)) -> -(all B_x c_Product__Type_OPair(T_a,T_a,B_x,B_x) != V_p_2))) # label(fact_IdE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 367 (all V_B_2 all V_A_2 all V_aa_2 all T_a ((c_member(T_a,V_aa_2,V_A_2) -> c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2))) & (-c_member(T_a,V_aa_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Int__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 368 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_trancl__rtrancl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 369 (all V_Q_2 all T_b all T_a all V_y_2 all V_x_2 all V_Pa_2 (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2) -> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))))) # label(fact_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 370 (all V_B_2 all V_A_2 all V_R_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_R_2,V_B_2)))) # label(fact_Image__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 371 (all V_x_2 all T_a V_x_2 = c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 372 (all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> -(all B_c (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,B_c),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_c,V_ba_2),V_r_2)))))) # label(fact_tranclE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 373 (all V_aa_2 all T_a -c_member(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_emptyE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 374 (all T_a c_Relation_OField(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Field__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 375 (all V_x_2 all T_b all T_a (class_Orderings_Obot(T_a) -> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_bot__apply) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 376 (all V_ba_2 all V_aa_2 all V_f_2 all T_a all T_c all T_b hAPP(V_f_2,c_Product__Type_OPair(T_b,T_c,V_aa_2,V_ba_2)) = c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2,V_aa_2,V_ba_2)) # label(fact_curry__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 377 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a c_Set_Oinsert(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)) = c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),V_r_2))) # label(fact_Domain__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 378 (all V_B_2 all V_C_2 all V_aa_2 all T_a (-c_member(T_a,V_aa_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 379 (all V_r_2 all T_a c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ORange(T_a,T_a,V_r_2)) # label(fact_trancl__range) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 380 (all V_R_2 all V_y_2 all V_x_2 all T_a (V_y_2 != V_x_2 & c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) | V_y_2 = V_x_2 <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))) # label(fact_rtrancl__eq__or__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 381 (all V_r_2 all T_a c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2)) # label(fact_total__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 382 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = V_x))) # label(fact_sup__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 383 (all V_Y_2 all V_X_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_Y_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> V_Y_2 = V_X_2 | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_quotient__disj) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 384 (all V_B_2 all T_a all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_less__by__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 385 (all V_x_2 all V_L_2 (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_x_2),c_Arrow__Order__Mirabelle_OLin))) # label(fact_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 386 (all V_r_2 all T_a (c_Wellfounded_Oacyclic(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)) <-> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclic__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 387 (all V_y_2 all V_x_2 all V_Q_2 all V_Pa_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))))) # label(fact_predicate2D) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 388 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__ge1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 389 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 390 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> (all B_x (c_member(T_a,B_x,V_A_2) -> (all B_xa (c_member(T_a,B_xa,V_B_2) -> B_xa != B_x)))))) # label(fact_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 391 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Diff__Int) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 392 (all V_B_2 all V_aa_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 393 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 394 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_y_2 = V_x_2))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 395 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_subset__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 396 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 397 (all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (V_aa_2 != V_ba_2 -> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,B_y),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_ba_2),V_r_2)))))) # label(fact_rtranclE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 398 (all V_Q_2 all V_Pa_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_Pa_2,V_Q_2))) -> ((all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,B_x),c_Transitive__Closure_Ortrancl(T_a,V_Pa_2)) -> (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_Q_2) -> B_x = B_y)))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_Pa_2))))) # label(fact_rtrancl__Un__separatorE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 399 (all V_x_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_x_2,V_A_2) -> c_member(T_a,V_x_2,V_B_2)))) # label(fact_set__mp) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 400 (all V_S_2 all V_R_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)))) # label(fact_rtrancl__Un__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 401 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_a (c_Relation_Osingle__valued(T_a,T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_z_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) | c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_single__valued__confluent) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 402 (all V_r_2 all T_b all V_ba_2 all T_a (c_member(T_a,V_ba_2,c_Relation_ORange(T_b,T_a,V_r_2)) -> -(all B_x -c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_ba_2),V_r_2)))) # label(fact_RangeE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 403 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_y = V_x)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 404 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_y = V_x -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 405 (all V_r_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2)) # label(fact_reflcl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 406 (all V_A_2 all V_C_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 407 (all V_B_2 all V_D_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_D_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Diff__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 408 (all V_r_2 all T_a c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))) # label(fact_rtrancl__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 409 (all V_R_2 all T_a (c_Wellfounded_Owf(T_a,V_R_2) -> c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)))) # label(fact_wf__in__rel) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 410 (all V_ba_2 all V_aa_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) # label(fact_equiv__class__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 411 (all V_A_2 all T_a V_A_2 = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_Int__absorb) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 412 (all V_Fa_2 ((all B_x (c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x,c_Arrow__Order__Mirabelle_OProf) -> (all B_a all B_b ((all B_i c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(B_x,B_i))) -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(V_Fa_2,B_x)))))) <-> c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2))) # label(fact_unanimity__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 413 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2)) <-> V_y_2 != V_z_2 & (V_x_2 = V_z_2 -> V_y_2 != V_x_2) & (V_x_2 != V_z_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)))) # label(fact_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 414 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_subset__refl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 415 (all V_r_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_r_2) <-> (all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_acyclic__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 416 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 417 (all V_r_2 all T_b all V_aa_2 all T_a (c_member(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)) -> -(all B_y -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,B_y),V_r_2)))) # label(fact_DomainE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 418 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) = hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2))) # label(fact_sup__apply) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 419 (all V_s_2 all V_B_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_Relation_Orefl__on(T_a,V_B_2,V_s_2) -> c_Relation_Orefl__on(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))))) # label(fact_refl__on__Int) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 420 (all V_ba_2 all V_aa_2 all V_c_2 all T_a all T_c all T_b c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_c_2,c_Product__Type_OPair(T_b,T_c,V_aa_2,V_ba_2)) = hAPP(hAPP(V_c_2,V_aa_2),V_ba_2)) # label(fact_internal__split__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 421 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 422 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 423 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 424 (all V_ba_2 all V_aa_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2)))) # label(fact_equiv__class__nondisjoint) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 425 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 426 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))))) # label(fact_distrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 427 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Opartial__order__on(T_a,V_A_2,V_r_2) & c_Relation_Ototal__on(T_a,V_A_2,V_r_2) <-> c_Order__Relation_Olinear__order__on(T_a,V_A_2,V_r_2))) # label(fact_linear__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 428 (all V_r_2 all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_quotient__is__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 429 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)) # label(fact_Un__assoc) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 430 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Olinear__order__on(T_a,V_A_2,V_r_2) <-> c_Order__Relation_Olinear__order__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2)))) # label(fact_linear__order__on__converse) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 431 (all V_a2_2 all V_a1_2 all V_Fa_2 all V_R_2 all T_b all T_a ((exists B_g ((all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(B_g,B_z)))) & hAPP(hAPP(V_Fa_2,B_g),V_a1_2) = hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2))) <-> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2,hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2)))) # label(fact_wfrec__rel_Oequations) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 432 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_B_2))) # label(fact_IntD2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 433 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))) # label(fact_inf__apply) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 434 (all T_2 all T_1 (class_Orderings_Obot(T_1) -> class_Orderings_Obot(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Obot) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 435 (all T_a c_Relation_Oantisym(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_antisym__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 436 (all V_Q_2 all V_Pa_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_Pa_2,V_Q_2))) -> ((all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_Pa_2)) -> (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_Q_2) -> B_x = B_y)))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),c_Transitive__Closure_Ortrancl(T_a,V_Pa_2))))) # label(fact_rtrancl__Un__separator__converseE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 437 (all V_r_2 all V_A_2 all T_a (c_Relation_Ototal__on(T_a,V_A_2,V_r_2) <-> (all B_x (c_member(T_a,B_x,V_A_2) -> (all B_xa (c_member(T_a,B_xa,V_A_2) -> (B_x != B_xa -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2) | c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)))))))) # label(fact_total__on__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 438 (all T_a c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_wf__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 439 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 440 (all V_z_2 all V_r_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_rtrancl__trancl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 441 (all V_A_2 all T_a ((exists B_x c_member(T_a,B_x,V_A_2)) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != V_A_2)) # label(fact_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 442 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_a) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 443 (all V_r_2 all V_ba_2 all V_aa_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OField(T_a,V_r_2)) = c_Relation_OField(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2))) # label(fact_Field__insert) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 444 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 445 (all V_r_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_rtrancl__converseD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 446 (all V_A_2 all T_a V_A_2 = c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_Range__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 447 (all V_y_2 all V_x_2 all V_R_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2) <-> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)))) # label(fact_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 448 (all V_B_2 all V_A_2 all T_a V_A_2 = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 449 (all V_A_2 all V_R_2 all T_a (c_Wellfounded_Owf(T_a,V_R_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Relation_OImage(T_a,T_a,V_R_2,V_A_2)) -> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2))) # label(fact_wfE__pf) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 450 (all V_r_2 all V_z_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (V_z_2 != V_x_2 -> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_y),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))))) # label(fact_converse__rtranclE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 451 (all V_r_2 all T_b all V_aa_2 all T_a (c_member(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)) <-> (exists B_y c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,B_y),V_r_2)))) # label(fact_Domain__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 452 (all V_r_2 all T_a (c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)) -> c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_wf__converse__trancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 453 (all V_x_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)))) # label(fact_acc__wfD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 454 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2)),c_Relation_ODomain(T_a,T_b,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Domain__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 455 (all V_A_2 all V_S_2 all V_R_2 all T_a all T_b c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_S_2,V_A_2)) = c_Relation_OImage(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_R_2,V_S_2),V_A_2)) # label(fact_Un__Image) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 456 (all V_S_2 all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)) = c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)))) # label(fact_rtrancl__Un__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 457 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 458 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Int__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 459 (all V_r_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = c_Equiv__Relations_Oquotient(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2)) # label(fact_quotient__empty) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 460 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 461 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 462 (all V_z_2 all V_y_2 all V_f_2 all V_r_2 all T_b all T_a (c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),V_r_2) -> hAPP(V_f_2,V_z_2) = hAPP(V_f_2,V_y_2)))) # label(fact_congruentD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 463 (all V_x_2 all V_Q_2 all V_Pa_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) -> (hBOOL(hAPP(V_Pa_2,V_x_2)) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 464 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 465 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)))))) # label(fact_le__infI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 466 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 467 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 468 (all V_r_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))))) # label(fact_trancl__converseI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 469 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (c_member(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,V_A_2)) -> (V_aa_2 != V_ba_2 -> c_member(T_a,V_aa_2,V_A_2)))) # label(fact_insertE) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 470 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclicI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 471 (all V_r_2 all V_aa_2 all T_a ((all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_aa_2),V_r_2) -> c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))) <-> c_member(T_a,V_aa_2,c_Wellfounded_Oacc(T_a,V_r_2)))) # label(fact_acc_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 472 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_y = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 473 (all V_c_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_ba_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_rtrancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 474 (all V_f_2 all T_b all V_r_2 all V_aa_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_aa_2),V_r_2) -> hAPP(V_f_2,V_x_2) = hAPP(c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_aa_2),V_x_2))) # label(fact_cut__apply) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 475 (all V_x_2 all V_aa_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_x_2),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_aa_2),V_r_2)))) # label(fact_wf__asym) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 476 (all V_A_2 all V_B_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnI2) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 477 (all T_a all V_B_2 all V_A_2 (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) <-> V_B_2 = V_A_2)) # label(fact_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 478 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__mono) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 479 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2),V_r_2) -> c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_ba_2,V_aa_2),c_Relation_Oconverse(T_a,T_b,V_r_2)))) # label(fact_converseI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 480 (all V_B_2 all V_A_2 all V_aa_2 all T_a (-c_member(T_a,V_aa_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 481 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_le__supI1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 482 (all V_A_2 all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_Int__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 483 (all V_ba_2 all V_aa_2 all T_b all T_a all V_f_2 (hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_aa_2,V_ba_2))) -> hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_aa_2,V_ba_2)))) # label(fact_curryI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 484 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 485 (all V_x_2 all V_r_2 all T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Oconverse(T_a,T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_x_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_irrefl__tranclI) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 486 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_inf1D1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 487 (all V_B_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Int__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 488 (all V_x_2 all V_Fa_2 all V_R_2 all T_a all T_b hAPP(hAPP(V_Fa_2,c_Recdef_Ocut(T_b,T_a,c_Nitpick_Owf__wfrec(T_b,T_a,V_R_2,V_Fa_2),V_R_2,V_x_2)),V_x_2) = c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_Fa_2,V_x_2)) # label(fact_Nitpick_Owf__wfrec_H__def) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 489 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 490 (all V_R2_2 all V_R1_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2)))) # label(fact_acc__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 491 (all V_aa_2 all V_r_2 all V_ba_2 all T_a (c_member(T_a,V_ba_2,c_Wellfounded_Oacc(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_ba_2),V_r_2) -> c_member(T_a,V_aa_2,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc__downward) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 492 (all V_aa_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_aa_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_aa_2,V_aa_2),V_r_2)))) # label(fact_refl__onD) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 493 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 494 (all V_r_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_r_2) -> c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_acyclic__impl__antisym__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.39/1.74 495 (all V_B_2 all V_A_2 all T_a all T_b c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2))) # label(fact_Range__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.39/1.78 496 (all V_p_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_p_2,V_r_2) -> c_Wellfounded_Owf(T_a,V_p_2)))) # label(fact_wf__subset) # label(axiom) # label(non_clause). [assumption]. 1.39/1.78 497 (all V_x all V_y all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.39/1.78 498 (all V_A_2 all V_aa_2 all T_a c_Set_Oinsert(T_a,V_aa_2,V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) # label(fact_insert__is__Un) # label(axiom) # label(non_clause). [assumption]. 1.39/1.78 499 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_B_2) | c_member(T_a,V_c_2,V_A_2) <-> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Un__iff) # label(axiom) # label(non_clause). [assumption]. 1.39/1.78 500 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnI1) # label(axiom) # label(non_clause). [assumption]. 1.39/1.78 501 -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption]. 1.39/1.78 1.39/1.78 ============================== end of process non-clausal formulas === 1.39/1.78 1.39/1.78 ============================== PROCESS INITIAL CLAUSES =============== 1.39/1.78 1.39/1.78 ============================== PREDICATE ELIMINATION ================= 1.39/1.78 502 class_Lattices_Osemilattice__sup(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 1.39/1.78 503 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),c_Lattices_Osemilattice__sup__class_Osup(A,C,E)) # label(fact_sup__mono) # label(axiom). [clausify(18)]. 1.39/1.78 504 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__supE) # label(axiom). [clausify(22)]. 1.39/1.78 505 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__supE) # label(axiom). [clausify(22)]. 1.39/1.78 506 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) = c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)) # label(fact_sup__left__commute) # label(axiom). [clausify(32)]. 1.39/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,D)). [resolve(502,a,503,a)]. 1.39/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(502,a,504,a)]. 1.39/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(502,a,505,a)]. 1.39/1.78 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,C)). [resolve(502,a,506,a)]. 1.39/1.79 507 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) # label(fact_sup_Oleft__idem) # label(axiom). [clausify(97)]. 1.39/1.79 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B). [resolve(507,a,502,a)]. 1.39/1.79 508 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) = c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)) # label(fact_sup_Oleft__commute) # label(axiom). [clausify(101)]. 1.39/1.79 509 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__sup(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom). [clausify(127)]. 1.39/1.79 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,F)). [resolve(509,b,503,a)]. 1.39/1.79 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E). [resolve(509,b,504,a)]. 1.39/1.79 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),D,E). [resolve(509,b,505,a)]. 1.39/1.79 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E)). [resolve(509,b,506,a)]. 1.39/1.79 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D). [resolve(509,b,507,a)]. 1.39/1.79 510 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,B) = B # label(fact_sup__idem) # label(axiom). [clausify(138)]. 1.39/1.79 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,A) = A. [resolve(510,a,502,a)]. 1.39/1.79 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,C) = C | -class_Lattices_Olattice(B). [resolve(510,a,509,b)]. 1.39/1.79 511 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__sup__iff) # label(axiom). [clausify(149)]. 1.39/1.79 512 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__sup__iff) # label(axiom). [clausify(149)]. 1.39/1.79 513 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__sup__iff) # label(axiom). [clausify(149)]. 1.39/1.79 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(513,a,502,a)]. 1.39/1.79 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D),E) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,E) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),D,E) | -class_Lattices_Olattice(B). [resolve(513,a,509,b)]. 1.39/1.80 514 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_le__supI) # label(axiom). [clausify(161)]. 1.39/1.80 515 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)) # label(fact_sup__ge2) # label(axiom). [clausify(204)]. 1.39/1.80 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,A)). [resolve(515,a,502,a)]. 1.39/1.80 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,C)) | -class_Lattices_Olattice(B). [resolve(515,a,509,b)]. 1.39/1.80 516 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_sup__least) # label(axiom). [clausify(239)]. 1.39/1.80 517 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,D,C)) # label(fact_le__supI2) # label(axiom). [clausify(255)]. 1.39/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,C,B)). [resolve(517,a,502,a)]. 1.39/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),E,D)) | -class_Lattices_Olattice(B). [resolve(517,a,509,b)]. 1.39/1.80 518 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(A,C,B) # label(fact_sup_Ocommute) # label(axiom). [clausify(310)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,A). [resolve(518,a,502,a)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,C) | -class_Lattices_Olattice(B). [resolve(518,a,509,b)]. 1.39/1.80 519 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) = c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_sup_Oassoc) # label(axiom). [clausify(311)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)). [resolve(519,a,502,a)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D),E) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,E)) | -class_Lattices_Olattice(B). [resolve(519,a,509,b)]. 1.39/1.80 520 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) != C | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__sup) # label(axiom). [clausify(312)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B) != B | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(520,a,502,a)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D) != D | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -class_Lattices_Olattice(B). [resolve(520,a,509,b)]. 1.39/1.80 521 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = C | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__sup) # label(axiom). [clausify(312)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B) = B | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(521,a,502,a)]. 1.39/1.80 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D) = D | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -class_Lattices_Olattice(B). [resolve(521,a,509,b)]. 1.39/1.81 522 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,B) = B # label(fact_sup_Oidem) # label(axiom). [clausify(324)]. 1.39/1.81 523 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) = c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_sup__assoc) # label(axiom). [clausify(326)]. 1.39/1.81 524 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(A,C,B) # label(fact_sup__commute) # label(axiom). [clausify(354)]. 1.39/1.81 525 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,C,B) = C # label(fact_sup__absorb1) # label(axiom). [clausify(382)]. 1.39/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,A) = B. [resolve(525,a,502,a)]. 1.39/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,C) = D | -class_Lattices_Olattice(B). [resolve(525,a,509,b)]. 1.39/1.81 526 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) # label(fact_sup__ge1) # label(axiom). [clausify(388)]. 1.39/1.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,A,B)). [resolve(526,a,502,a)]. 1.39/1.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D)) | -class_Lattices_Olattice(B). [resolve(526,a,509,b)]. 1.39/1.81 527 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) # label(fact_sup__left__idem) # label(axiom). [clausify(396)]. 1.39/1.81 528 class_Lattices_Osemilattice__sup(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 1.39/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,D)). [resolve(528,a,503,a)]. 1.39/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(528,a,504,a)]. 1.39/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,B,C). [resolve(528,a,505,a)]. 1.39/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C)). [resolve(528,a,506,a)]. 1.39/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B). [resolve(528,a,507,a)]. 1.39/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,A) = A. [resolve(528,a,510,a)]. 1.39/1.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,B,C). [resolve(528,a,513,a)]. 1.39/1.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A)). [resolve(528,a,515,a)]. 1.39/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,C,B)). [resolve(528,a,517,a)]. 1.39/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A). [resolve(528,a,518,a)]. 1.39/1.86 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(528,a,519,a)]. 1.39/1.86 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) != B | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(528,a,520,a)]. 1.39/1.86 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = B | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(528,a,521,a)]. 1.39/1.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A) = B. [resolve(528,a,525,a)]. 1.39/1.86 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B)). [resolve(528,a,526,a)]. 1.39/1.86 529 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = C # label(fact_sup__absorb2) # label(axiom). [clausify(472)]. 1.39/1.86 530 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_le__supI1) # label(axiom). [clausify(481)]. 1.39/1.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat,B,C)). [resolve(530,a,502,a)]. 1.39/1.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,E)) | -class_Lattices_Olattice(B). [resolve(530,a,509,b)]. 1.39/1.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(530,a,528,a)]. 1.39/1.86 531 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption]. 1.39/1.86 532 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__cases) # label(axiom). [clausify(20)]. 1.39/1.86 533 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__linear) # label(axiom). [clausify(355)]. 1.39/1.86 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(531,a,532,a)]. 1.39/1.86 534 -c_Arrow__Order__Mirabelle_OIIA(A) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 535 c_Arrow__Order__Mirabelle_OIIA(v_F) # label(fact_assms_I3_J) # label(axiom). [assumption]. 1.39/1.86 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(A,f42(v_F,A,B,C,D))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(B,f42(v_F,A,B,C,D))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,A)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,B)). [resolve(534,a,535,a)]. 1.39/1.86 536 -c_Arrow__Order__Mirabelle_OIIA(A) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(A,f42(v_F,A,B,C,D))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(B,f42(v_F,A,B,C,D))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,A)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,B)). [resolve(536,a,535,a)]. 1.39/1.86 537 -c_Arrow__Order__Mirabelle_OIIA(A) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(A,f42(v_F,A,B,C,D))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(B,f42(v_F,A,B,C,D))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,A)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,B)). [resolve(537,a,535,a)]. 1.39/1.86 538 -c_Arrow__Order__Mirabelle_OIIA(A) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(A,f42(v_F,A,B,C,D))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(B,f42(v_F,A,B,C,D))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,A)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,D),hAPP(v_F,B)). [resolve(538,a,535,a)]. 1.39/1.86 539 c_Arrow__Order__Mirabelle_OIIA(A) | c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f43(A),c_Arrow__Order__Mirabelle_OProf) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f43(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(539,a,534,a)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f43(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(539,a,536,a)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f43(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(539,a,537,a)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f43(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(539,a,538,a)]. 1.39/1.86 540 c_Arrow__Order__Mirabelle_OIIA(A) | c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f44(A),c_Arrow__Order__Mirabelle_OProf) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f44(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(540,a,534,a)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f44(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(540,a,536,a)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f44(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(540,a,537,a)]. 1.39/1.86 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f44(A),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(540,a,538,a)]. 1.39/1.86 541 c_Arrow__Order__Mirabelle_OIIA(A) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.86 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(541,a,534,a)]. 1.39/1.86 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(541,a,536,a)]. 1.39/1.86 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(541,a,537,a)]. 1.39/1.87 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(541,a,538,a)]. 1.39/1.87 542 c_Arrow__Order__Mirabelle_OIIA(A) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(542,a,534,a)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(542,a,536,a)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(542,a,537,a)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f43(A),B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(f44(A),B)) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),D,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(C,f42(A,C,D,E,F))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(D,f42(A,C,D,E,F))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,C)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,E,F),hAPP(A,D)). [resolve(542,a,538,a)]. 1.39/1.87 543 c_Arrow__Order__Mirabelle_OIIA(A) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(543,a,534,a)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(543,a,536,a)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(543,a,537,a)]. 1.39/1.87 Derived: c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(543,a,538,a)]. 1.39/1.87 544 c_Arrow__Order__Mirabelle_OIIA(A) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) # label(fact_IIA__def) # label(axiom). [clausify(189)]. 1.39/1.87 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(544,a,534,a)]. 1.39/1.87 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(544,a,536,a)]. 1.39/1.87 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(544,a,537,a)]. 1.39/1.92 Derived: -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f43(A))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f45(A),f46(A)),hAPP(A,f44(A))) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(B,f42(A,B,C,D,E))) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(C,f42(A,B,C,D,E))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,B)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,D,E),hAPP(A,C)). [resolve(544,a,538,a)]. 1.39/1.92 545 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__bot) # label(axiom). [assumption]. 1.39/1.92 546 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Obot__class_Obot(A)) = B # label(fact_sup__bot__right) # label(axiom). [clausify(57)]. 1.39/1.92 547 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Obot__class_Obot(A)) = c_Orderings_Obot__class_Obot(A) # label(fact_inf__bot__right) # label(axiom). [clausify(152)]. 1.39/1.92 548 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != B | c_Orderings_Obot__class_Obot(A) != C | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Orderings_Obot__class_Obot(A) # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(234)]. 1.39/1.92 549 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = B | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) != c_Orderings_Obot__class_Obot(A) # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(234)]. 1.39/1.92 550 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = B | c_Lattices_Osemilattice__sup__class_Osup(A,C,B) != c_Orderings_Obot__class_Obot(A) # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(234)]. 1.39/1.92 551 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Obot__class_Obot(A),B) = c_Orderings_Obot__class_Obot(A) # label(fact_inf__bot__left) # label(axiom). [clausify(279)]. 1.39/1.92 552 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Obot__class_Obot(A),B) = B # label(fact_sup__bot__left) # label(axiom). [clausify(289)]. 1.39/1.92 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = A. [resolve(545,a,546,a)]. 1.39/1.92 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(545,a,547,a)]. 1.39/1.92 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != A | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != B | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(545,a,548,a)]. 1.39/1.95 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) != c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(545,a,549,a)]. 1.39/1.95 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A) != c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(545,a,550,a)]. 1.39/1.95 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),A) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(545,a,551,a)]. 1.39/1.95 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),A) = A. [resolve(545,a,552,a)]. 1.39/1.95 553 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__bot(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom). [clausify(489)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Orderings_Obot__class_Obot(tc_fun(B,A))) = C. [resolve(553,b,546,a)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Orderings_Obot__class_Obot(tc_fun(B,A))) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(553,b,547,a)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != C | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != D | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(553,b,548,a)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) != c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(553,b,549,a)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C) != c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(553,b,550,a)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Orderings_Obot__class_Obot(tc_fun(B,A)),C) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(553,b,551,a)]. 1.39/1.95 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),c_Orderings_Obot__class_Obot(tc_fun(B,A)),C) = C. [resolve(553,b,552,a)]. 1.39/1.95 554 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__inf(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom). [clausify(393)]. 1.39/1.95 555 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B) # label(fact_inf__le1) # label(axiom). [clausify(84)]. 1.39/1.95 556 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__greatest) # label(axiom). [clausify(89)]. 1.39/1.95 557 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf__left__idem) # label(axiom). [clausify(96)]. 1.39/1.95 558 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__infE) # label(axiom). [clausify(109)]. 1.39/1.95 559 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__infE) # label(axiom). [clausify(109)]. 1.39/1.95 560 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_inf__absorb1) # label(axiom). [clausify(120)]. 1.39/1.95 561 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),c_Lattices_Osemilattice__inf__class_Oinf(A,C,E)) # label(fact_inf__mono) # label(axiom). [clausify(141)]. 1.39/1.95 562 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf_Oidem) # label(axiom). [clausify(158)]. 1.39/1.95 563 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf_Oleft__idem) # label(axiom). [clausify(163)]. 1.39/1.95 564 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf__idem) # label(axiom). [clausify(167)]. 1.39/1.95 565 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf__commute) # label(axiom). [clausify(176)]. 1.39/1.95 566 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf_Oassoc) # label(axiom). [clausify(198)]. 1.39/1.95 567 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf__left__commute) # label(axiom). [clausify(209)]. 1.39/1.95 568 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__assoc) # label(axiom). [clausify(229)]. 1.39/1.95 569 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C) # label(fact_le__infI1) # label(axiom). [clausify(252)]. 1.39/1.95 570 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) = B # label(fact_inf__absorb2) # label(axiom). [clausify(327)]. 1.39/1.95 571 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C) # label(fact_inf__le2) # label(axiom). [clausify(328)]. 1.39/1.95 572 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__inf__iff) # label(axiom). [clausify(333)]. 1.39/1.95 573 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__inf__iff) # label(axiom). [clausify(333)]. 1.39/1.95 574 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,D,C)) # label(fact_le__inf__iff) # label(axiom). [clausify(333)]. 1.39/1.95 575 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_le__iff__inf) # label(axiom). [clausify(346)]. 1.39/1.95 576 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) != B # label(fact_le__iff__inf) # label(axiom). [clausify(346)]. 1.39/1.95 577 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf_Oleft__commute) # label(axiom). [clausify(359)]. 1.39/1.95 578 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C) # label(fact_le__infI2) # label(axiom). [clausify(365)]. 1.39/1.95 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),C). [resolve(554,b,555,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)). [resolve(554,b,556,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D). [resolve(554,b,557,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D). [resolve(554,b,558,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E). [resolve(554,b,559,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = C. [resolve(554,b,560,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,F)). [resolve(554,b,561,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,C) = C. [resolve(554,b,562,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C). [resolve(554,b,565,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),E) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)). [resolve(554,b,566,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E)). [resolve(554,b,567,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),D). [resolve(554,b,569,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C) = C. [resolve(554,b,570,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),D). [resolve(554,b,571,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) != C. [resolve(554,b,576,a)]. 1.39/1.96 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),E,C),D). [resolve(554,b,578,a)]. 1.39/1.96 579 class_Lattices_Osemilattice__inf(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 1.39/1.96 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),A). [resolve(579,a,555,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(579,a,556,a)]. 1.39/1.96 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B). [resolve(579,a,557,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(579,a,558,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(579,a,559,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = A. [resolve(579,a,560,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,D)). [resolve(579,a,561,a)]. 1.39/1.96 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,A) = A. [resolve(579,a,562,a)]. 1.39/1.96 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A). [resolve(579,a,565,a)]. 1.39/1.96 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(579,a,566,a)]. 1.39/1.96 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C)). [resolve(579,a,567,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),B). [resolve(579,a,569,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A) = A. [resolve(579,a,570,a)]. 1.39/1.96 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),B). [resolve(579,a,571,a)]. 1.39/1.96 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) != A. [resolve(579,a,576,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B). [resolve(579,a,578,a)]. 1.39/1.96 580 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf_Ocommute) # label(axiom). [clausify(442)]. 1.39/1.96 581 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__infI) # label(axiom). [clausify(465)]. 1.39/1.96 582 class_Lattices_Osemilattice__inf(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 1.39/1.96 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),A). [resolve(582,a,555,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)). [resolve(582,a,556,a)]. 1.39/1.96 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B). [resolve(582,a,557,a)]. 1.39/1.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(582,a,558,a)]. 1.39/2.02 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(582,a,559,a)]. 1.39/2.02 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) = A. [resolve(582,a,560,a)]. 1.39/2.02 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,D)). [resolve(582,a,561,a)]. 1.39/2.02 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,A) = A. [resolve(582,a,562,a)]. 1.39/2.02 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,A). [resolve(582,a,565,a)]. 1.39/2.02 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)). [resolve(582,a,566,a)]. 1.39/2.02 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C)). [resolve(582,a,567,a)]. 1.39/2.02 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),B). [resolve(582,a,569,a)]. 1.39/2.02 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,A) = A. [resolve(582,a,570,a)]. 1.39/2.02 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),B). [resolve(582,a,571,a)]. 1.39/2.02 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) != A. [resolve(582,a,576,a)]. 1.39/2.02 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,C,A),B). [resolve(582,a,578,a)]. 1.39/2.02 583 c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,B),C) | -c_Nitpick_Orefl_H(A,C) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(107)]. 1.39/2.02 584 -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f20(B,A),f20(B,A)),B) | c_Nitpick_Orefl_H(A,B) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(107)]. 1.39/2.02 Derived: c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,B),C) | -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f20(C,A),f20(C,A)),C). [resolve(583,b,584,b)]. 1.39/2.02 585 c_Arrow__Order__Mirabelle_Odictator(A,B) | c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f33(B,A),c_Arrow__Order__Mirabelle_OProf) # label(fact_dictator__def) # label(axiom). [clausify(171)]. 1.39/2.02 586 -c_Arrow__Order__Mirabelle_Odictator(A,B) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | hAPP(A,C) = hAPP(C,B) # label(fact_dictator__def) # label(axiom). [clausify(171)]. 1.39/2.02 Derived: c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f33(A,B),c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | hAPP(B,C) = hAPP(C,A). [resolve(585,a,586,a)]. 1.39/2.02 587 c_Arrow__Order__Mirabelle_Odictator(A,B) | hAPP(A,f33(B,A)) != hAPP(f33(B,A),B) # label(fact_dictator__def) # label(axiom). [clausify(171)]. 1.39/2.02 Derived: hAPP(A,f33(B,A)) != hAPP(f33(B,A),B) | -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),C,c_Arrow__Order__Mirabelle_OProf) | hAPP(A,C) = hAPP(C,B). [resolve(587,a,586,a)]. 1.39/2.07 588 -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(A,f83(D,A,B,C))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(D,A)) | -c_Arrow__Order__Mirabelle_Ounanimity(D) # label(fact_unanimity__def) # label(axiom). [clausify(412)]. 1.39/2.07 589 c_Arrow__Order__Mirabelle_Ounanimity(v_F) # label(fact_u) # label(axiom). [assumption]. 1.39/2.07 590 c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f80(A),c_Arrow__Order__Mirabelle_OProf) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(412)]. 1.39/2.07 591 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f81(A),f82(A)),hAPP(f80(A),B)) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(412)]. 1.39/2.07 592 -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f81(A),f82(A)),hAPP(A,f80(A))) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(412)]. 1.39/2.07 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(A,f83(v_F,A,B,C))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(v_F,A)). [resolve(588,d,589,a)]. 1.39/2.07 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(A,f83(D,A,B,C))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(D,A)) | c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),f80(D),c_Arrow__Order__Mirabelle_OProf). [resolve(588,d,590,b)]. 1.39/2.07 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(A,f83(D,A,B,C))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(D,A)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f81(D),f82(D)),hAPP(f80(D),E)). [resolve(588,d,591,b)]. 1.39/2.07 Derived: -c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),A,c_Arrow__Order__Mirabelle_OProf) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(A,f83(D,A,B,C))) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),hAPP(D,A)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f81(D),f82(D)),hAPP(D,f80(D))). [resolve(588,d,592,b)]. 2.13/2.43 593 -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,B),C) | -c_Relation_Oirrefl(A,C) # label(fact_irrefl__def) # label(axiom). [clausify(238)]. 2.13/2.43 594 c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f58(B,A),f58(B,A)),B) | c_Relation_Oirrefl(A,B) # label(fact_irrefl__def) # label(axiom). [clausify(238)]. 2.13/2.43 Derived: -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,B),C) | c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f58(C,A),f58(C,A)),C). [resolve(593,b,594,b)]. 2.13/2.43 595 c_Wellfounded_Owf(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,c_Relation_OId(A))) | -c_Order__Relation_Owell__order__on(A,C,B) # label(fact_well__order__on__def) # label(axiom). [clausify(242)]. 2.13/2.43 596 -c_Wellfounded_Owf(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,c_Relation_OId(A))) | -c_Order__Relation_Olinear__order__on(A,C,B) | c_Order__Relation_Owell__order__on(A,C,B) # label(fact_well__order__on__def) # label(axiom). [clausify(242)]. 2.13/2.43 597 c_Order__Relation_Olinear__order__on(A,B,C) | -c_Order__Relation_Owell__order__on(A,B,C) # label(fact_well__order__on__def) # label(axiom). [clausify(242)]. 2.13/2.43 598 c_Order__Relation_Owell__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))) # label(fact_well__order__on__empty) # label(axiom). [clausify(300)]. 2.13/2.43 Derived: c_Wellfounded_Owf(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(598,a,595,b)]. 2.13/2.43 Derived: c_Order__Relation_Olinear__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))). [resolve(598,a,597,b)]. 2.13/2.43 2.13/2.43 ============================== end predicate elimination ============= 2.13/2.43 2.13/2.43 Auto_denials: (non-Horn, no changes). 2.13/2.43 2.13/2.43 Term ordering decisions: 2.13/2.43 Function symbol KB weights: tc_Arrow__Order__Mirabelle_Oalt=1. tc_HOL_Obool=1. c_Arrow__Order__Mirabelle_OProf=1. tc_Arrow__Order__Mirabelle_Oindi=1. tc_Nat_Onat=1. v_F=1. c_Arrow__Order__Mirabelle_OLin=1. v_a_H____=1. v_b____=1. v_a____=1. v_b_H____=1. v_P_H____=1. v_P____=1. c1=1. tc_prod=1. tc_fun=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Relation_OField=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Set_Othe__elem=1. c_Wellfounded_Omeasure=1. f15=1. f17=1. f20=1. f24=1. f30=1. f31=1. f33=1. f38=1. f39=1. f52=1. f53=1. f58=1. f72=1. f84=1. f92=1. f95=1. f97=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. c_fequal=1. f43=1. f44=1. f45=1. f46=1. f80=1. f81=1. f82=1. c_Lattices_Osemilattice__sup__class_Osup=1. c_Lattices_Osemilattice__inf__class_Oinf=1. c_Set_Oinsert=1. c_Relation_Oconverse=1. c_Groups_Ominus__class_Ominus=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_Equiv__Relations_Oquotient=1. c_FunDef_Oin__rel=1. c_Wellfounded_Omlex__prod=1. f5=1. f6=1. f7=1. f13=1. f21=1. f22=1. f23=1. f26=1. f27=1. f28=1. f40=1. f41=1. f50=1. f54=1. f74=1. f75=1. f90=1. f91=1. f96=1. c_Product__Type_OPair=1. c_Relation_OImage=1. c_Recdef_Owfrec=1. c_Relation_Oinv__image=1. c_Wellfounded_Olex__prod=1. c_Recdef_Osame__fst=1. c_Nitpick_Owf__wfrec=1. f1=1. f8=1. f9=1. f10=1. f14=1. f16=1. f29=1. f32=1. f47=1Alarm clock 179.12/180.01 Prover9 interrupted 179.12/180.02 EOF